Talk:Decimal/Archive 1

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Archive 1

Archive 2

The article claims that we use decimal numbering because humans have 10 fingers. I find this claim highly suspect: 10 fingers is sufficent to count in base 11 (just as one finger is sufficent to count in base 2). Does someone have a good citation for this? --Gmaxwell 20:33, 22 May 2005 (UTC)

I don't have the citation you request, but I think it's a very sensible claim even without documentation. A few things I find relevant:

• Base 10 in number words is older than base 10 in a positional number system.
• Try teaching a child (age 4-7) to count-in-11's using the fingers of two hands; then (when you have despaired) try teaching counting-in-10's instead. Or try teaching counting-in 6'5 and counting-in-5's using one hand only.

Right. 10 fingers. 0 (no fingers) 1,2,3,4,5,6,7,8,9,10 ... Which is all of the single digit symbols in base 11. Really. Base-11 is more obvious for hand counting than base-10, as long as you have a concept of zero. --Gmaxwell 22:35, 23 May 2005 (UTC)

• The chinese abacus has 5 beads on each wire to represent values 0-4 (the 5th being used only temporarily in calculations). The japanese abacus is similar but has done away with the extra beads, at the expense of making its use slightly harder to learn.

Right, I know how to use a chinese abacus. I'm not following how it helps this argument. ... Thanks for replying though... I honestly didn't expect a reply anytime soon! --Gmaxwell 22:35, 23 May 2005 (UTC)

Zero is an artificial mathematical symbol, unnatural for human perception. "Decimal" does not *necesarily* imply that 10 is spelled using two symbols. When you start counting fingers, 10 ranks the same as each of the 1 to 9 numerals. So, why ten and not eleven? Try to quickly show the number 30 by flashing your fingers. It's as natural as... 123. Now, try with 33. Still think that base eleven suits your fingers? Luciand 15:50, 29 December 2005 (UTC)

I am not really happy with the current TOC:

Contents

    * 1 Decimal notation
          o 1.1 Alternative notations
          o 1.2 Decimal fractions
          o 1.3 Other rational numbers
          o 1.4 Real numbers
    * 2 History
          o 2.1 Decimal writers
    * 3 See also
    * 4 External links

The article is about decimal notation, so it does not make sense (to me) to have a section titled "decimal notation". And even if it is there, I don't see why one should have a subsection called "Alternative notation". That should be its own section, preferably at the bottom, as it is a related topic to decimal notation, but not the focus of the article. Comments? Oleg Alexandrov (talk) 00:54, 22 February 2006 (UTC)

I failed the article for two reasons:

1. The "probably due to ten fingers" and "probably due to 20 fingers and toes" make sense, but they need to be cited... unfortunately we're not allowed to make inferences.
2. More importantly, the Grouping of digits section needs text. A link to another article doesn't cut it.

After that is done, feel free to renominate it at any time. Titoxd^{(?!? - cool stuff)} 18:40, 27 April 2007 (UTC)

One should note that Multiplication and Division take part in different parts of the brain (see Butterworth "The Mathematical Brain". and by separate processes. Multiplication is closer to animate numbers (such as other animals recognise), division more distant.

While a single method of counting is reckoned (a count of batches), there are many different division systems. The simple representation of numbers can be shown on a stone-board, where N stones in one column becomes 1 stone in the right. The most common form of number is the alternating system, where one replaces M stones for a single stone in the row above, and D stones in the top row for a single stone in the bottom row, one to the right. M is usually a number of count (eg 5, 10), where D is usually a division number (2, 4, 6, 8, 12). The chinese abacus is D=2 over M=5.

A precusros for an alternating system is a system of stand-alone fractions in D. This is known of the sumerians, and of the romans, but not elsewhere. However, the roman uncia is probably not the source of the germanic 100 of vi score.

One sees that many different systems become apparant eg 20 = 4*5 or 2*10, 40=4*10, 60=6*10, 120=12*10 are all historically known. The inherent 'decimal' system is seen, except that some have '5' at that point. To some extent, these arise by "making things bigger". The prehistory of 60 is 3*20. [O. Neugebauer - the exact sciences in ancient times]

Fractions are more complex. One has the Greek system (also mayan), where one makes ratio, eg 1944 parts where 2000 make the English foot, or the Roman weight-fractions (an uncia of weight, length and time, and number = 1/2, whence ounce and inch). One sees from their measurement systems, an ace (1) is variously a foot, a pound and a grain, and that these are invariably decimally counted (centar = 100 lb, millier = 1000 lb, mile = 100 paces), but divided approximately duodecimally (eg uncia = 1/12).

The sexagesimal numbers form the sumerian division system, these being to avoid division. For example, the most significant column is on the right, and subsequent places are divisions of the first. Zeros occur where they add meaning (eg leading, medially), but not finally, so 3 and 0 3 are different (3 and 1/20 respectively), but 3 0 is the same as 3 (ie as we write 3 vs 3.0). The count of numbers in the common system is the motely collection of decimal, sexagesimal etc (eg 192 = 100 60 30 2) See eg O Neugebaur.

That the system is a system for divisions is seen by the contents of the reckoners that come to us: tables of multiples of x by 1..20, 40, and tables of recriprocals (in ascending order logrithmically over sixty). The method of calculation was to determine the recriprocal and then look up these in the reckoners. (x = 44:26.40 exists, because this is 1/81.] We further note the existance of papers of the style of 'the problem of seven brothers' exist, giving 1/7 lieing between 0:8 34 16 and : 8 34 18, supporting the notion that it is indeed a system for fractions.

Sixty spread, along with the astronomy it used, both eastwards to India etc and westwards to Europe etc.

We see this fantasy with the duodecimal system. Historically, 12 is a division number, and that dozens and grosses were "super-divisions", ie measures, that on division, will reveal a unit peice. We have a grocer as one who deals in grosses, and sells off dozens and units.

The use of 10-like numbers (8, 12, 14, 16), is more to do with the recently devised method of using tables (the first tables, along with the first modern 0, appeare in late greece, and spread by the muslims to india and europe.

Wendy.krieger (talk) 06:35, 2 June 2008 (UTC)

I think we should start using the unambiguous word aal instead of decimal, because every base is decimal in its own base. Actually every time we say "base 10" we should say "base A" instead.

In this way we would always represent the base with the first digit that is not used for that base eg.:

base 2 ( = 10 in base 2) -> digits 0,1

base 3 ( = 10 in base 3) -> digits 0,1,2

base 9 ( = 10 in base 9) -> digits 0,1,2,3,4,5,6,7,8

base A ( = 10 in base A) -> digits 0,1,2,3,4,5,6,7,8,9

base B ( = 10 in base B) -> digits 0,1,2,3,4,5,6,7,8,9,A

I've been thinking about this for years, so I hope you all will agree with me on this.

--Ortonormale 00:47, 2005 May 11 (UTC)

It may be good to remember that the root "deci" means ten and "a" is a letter that is not associated with the base ten number system (why add another thing to confuse people?). Besides, saying "aal" would be more ambiguous than saying "Decimal". It sounds the same as "all" -Michael

very funny. but

• what comes after the zal base?
• I disagree, not every but only the aal system is decimal. "decimal" does not mean "digit 1 followed by digit 0"! you contradict yourself! — MFH: Talk 21:12, 11 May 2005 (UTC)

Yes, you would be right. I mean that since the discovery of base conversion, numerals have acquired new meanings while losing the direct link to their etymology. We could say that a new abstract level has been introduced between the original etymological meaning and the new virtual meaning. For example: 11 in base 2 represents the same quantity represented by 3 in base 8. Luckily or unluckily (according to your point of view) we have not a different set of names for each numeral in each base, therefore we have two possibilities:

• we can spell each numeral in every base but the base A (really sad)
  
• we can extend the same language structure we already use for base A to all bases up to Z.

In this latter case, we could simply say "eleven" to read the numeral 11 in whichever base. The same concept would apply to "ten", "decimal" and "digit".
Obviously, we would have ambiguities when not specifying the actual base, but this already happens when writing.
Nothing really fun so far. The funny part comes when we want to read numbers like

• APPLE that is: "aytypee thousand pee hundred eltyee"
• CRAZY that is: "ceetyar thousand ay hundred zeewy"
• SPELLING that is: "espee million ee hundred eltyel thousand i hundred entyjee"
• DECIMAL that is: "dee million ee hundred ceetyi thousand em hundred aytyel"

Again: obviously (as you have noticed) we would have an obstacle to complexity increase trying to use bases that are greater than Z, but this already happens when writing. It is a common problem for non positional numbering systems, but a simple solution consists in grouping. So for example we could use the base 2xG (or simply 2G) in which each digit is represented by a group of 2 digits in base G, like

• 20 08,
  • simply spelled "two zero blank zero eight" or
  • spelled-read "twenty zerotyeight" or
  • read "twentytyzerotyeight"
• A5 47 FF 00,
  • simply spelled "ay five blank four seven blank ef ef blank zero zero"
  • spelled-read "aytyfive fourtyseven eftyef zerotyzero"
  • read "aytyfive thousandty fourtyseven hundredty eftyeftyzeroty"

--Ortonormale 00:22, 2005 May 19 (UTC)

I find it totally meaningless. Don't confuse numbers and notations. Ten is ten, the number of circles in oooooooooo whichever base you use. Likewise, decimal always means base ten. What 10 means depends on the base, but decimal is default. No one would call (10)₂ ten. It's two. - TAKASUGI Shinji 06:25, 2005 May 19 (UTC)

Old English, Gothic, etc had words for reckoning by counts of ten (short count, or teentywise), vs the reckoning by base 120 (long count, twelftywise). Where several bases are in use concurrently, one might use neutral names, or names that have a common scheme, to describe the various notations. Where some are technical in nature (eg hexadecimal), the name would be described in the main base.

I use 'radix or base notation', for the expression of fractions &c by an implied added fraction, such as 'decimal fractions'. On the other hand, if i want to deliberately infer the denominator is 10 (rather than 60 or 120), i might call it a decimal. The point separating the fraction from the whole, is the 'radix', or root point

10 is ultimately derived from te.hund = two hands. If ye envisage a population that is heptadactic, you might correctly infer that two hands makes 14. The notion that 100 = 10 * 10 is not always the case. As long as there is a sequence of progression, the columns can tick over after different values. Historically, the column left of the units might be different to the other columns (eg mayan long count of days, has 20,20,...,20,18,20.

It is known in English metrology (see R E Zupko: A Dictionary of English Units to the Eighteenth Century: entry hundred), that writing something like C or 100 or hundred, might need to be qualified, eg 300, where C = v^xx xii , that is, 336.

Wendy.krieger (talk) 07:03, 5 June 2008 (UTC)

Is there any other theory at all for explaining the decimal system?

From a mathematical point of view, I see no argument that could be made for ten - two (or powers of two) is special, of course, since it's the smallest possible base (powers of two are just a neat way of cramming several binary digits into one handy symbol), three would give you balanced ternary, and I believe you can formalise the fact that 12 has a large number of factors.

Of course, it's possible that there might be a psychological aspect that makes 10 a natural choice, or that it was just an accident of history, but in the absence of support for either of those theories, maybe we should state this a bit more strongly?

RandomP 18:51, 13 May 2006 (UTC)

The words for five and hand are related in many languages, especially in New Guinean languages. And ten or twenty is called as a person in some languages. That strongly suggests our ancestors counted their fingers. How easy division will be is pointless - counting is much older than division. Languages of base-6 (Ndom), base-8 (Yuki), base-15 (Huli), and base-24 (Kakoli) have been reported.

Source:

• The Work of Glendon Lean on the Counting Systems of Papua New Guinea and Oceania
• What We Can Learn From the Counting Systems Research of Dr. Glendon Lean

- TAKASUGI Shinji 14:33, 15 May 2006 (UTC)

Thanks. Certainly interesting to know, but note that my question was whether there is any other theory for the use of ten, other than that that happens to be the number of non-thumb fingers.

RandomP 15:21, 15 May 2006 (UTC)

Gee, counting "non-thumb fingers" would lead us to use base 8 among most members of my species. Anyway, the mention of bases 6, 15, and 24 suggest the human predisposition to finger use is not absolutely overwhelming. -R. S. Shaw 18:55, 15 May 2006 (UTC)

Oops, sorry. I meant to say "fingers including thumbs", but got confused. Nothing to do with my extra pinkies, I assure you. RandomP 23:03, 15 May 2006 (UTC)

New Guinea, the most linguistically diverse area in the world, have various bases such as 4, 5, 6, 10, 15, 20, and 24. Body-part tally systems are also common. Eurasia is almost unified under decimal, with scattered vigesimal systems in its outer rim - Celtic languages, Basque, Caucasian languages, Dravidian languages, Burushaski, Ainu, etc. That suggests decimal spread and overwhelmed other bases in Eurasia. It seems to me China was the origin of decimal, because it has had a strict decimal system from the beginning while many other languages have special words for teens and decades. - TAKASUGI Shinji 00:18, 16 May 2006 (UTC)

I'm almost positive that the decimal system is the most widely used numeral system in the world for any reason but our fingers. Can anyone get any evidence to back this up? —Preceding unsigned comment added by 24.45.212.65 (talk) 07:18, 10 September 2008 (UTC)

A system based on fours and eights would correspond not to the fingers, but the spaces between the figures. The Indogermanic word for /nine/ and /new/ both come from a common stem, being the new number (of a group of four). One notes also that there are languages that change the style of counting at a multiple of four (English, two-left, three-ten), in french, between 16 and 17, and in fininsh between eight and nine (one before ten).

The sumerian counting system is evidently based on three scores (in very ancient times), but went through a phase where the sixths had fractional names (ie symbols for 1/6, ..., 5/6), before becoming a system of repeated divisions. One notes with Oppenheimer that the most famous system is a division system, to avoid having to do division. The numbers were not used in the usual multiplication sense (that 1.0 meant 60), but there is a distinction between 1, (eg 1 degree) vs 0.1 (1 minute), and 0.0.1 (1 second). Zero is known in this sense (the actual symbol also means sentence-period or full-stop).

For larger numbers, they used the usual motley collection of mixed decimal and sexagesimal (and some twelfty), so a number we write as 192, would be consistently be shown as 3A2 (ie 3.12) in the tables, in the attached matter might be shown as CIxxxii, that is, 100+60+3*10+2*1, ie 'one hundred and sixty-thirty-two', cf french, un cent, quatre-vingt-douze (100, 4-score and 12). --Wendy.krieger (talk) 08:10, 11 September 2008 (UTC)

The article confuses base 10 with positional systems. Someone commented on this above, but was never answered. If there is no discussion here, I'll go ahead and rewrite the article.

Chinese numerals are decimal, even though they're not positional. Likewise, Roman numerals are also decimal, though with a minor auxiliary base in 5. Hebrew gematria are decimal. There are very few written systems which are not decimal—Mayan and Babylonian are the only ones which comes to mind—though of course in spoken languages there are all kinds of bases and base combinations.

Besides decimal numeration, there are decimal fractions. All this requires is extending base 10 to fractional notation, though in practice in the modern world it nearly always implies a positional system. (Roman combined decimal numeration with duodecimal fractions, neither of which were positional.) India did not invent decimal numeration, which is the most common in the world, and AFAIK did not invent decimal fractions either; it invented the positional system and the zero that went along with it. (Mayans had a zero but not a fully positional system, due perhaps to religious considerations.) kwami (talk) 02:44, 26 February 2009 (UTC)

Most number systems from the ancient world make sense when these are read off a two-row (or alternating) abacus. The number systems are various attempts to record the count of stones, with some abbreviations. The main systems are

• Repetition of symbols (eg 70 = LXX [Roman, Greek] or sumerian - and | arrows (to form the digits). The egyptians used only the lower row, and so repetitions to 9 are not unknown. Empty columns are typically unrepresented since denominations do this, but zero is used for an empty count.
• Demotic style (ie symbol for 70, 76 as 70 6.) This can be overlayed with the alphabet (ancient or modern), to give alphabetic numbers of hebrew, greek and gothic systems.
• Digit + unit, in the style of 1h 6t 4 (for 164). Used by Mayans and by Chinese. In the mayan, the short form of the digit (sticks+stones) were attached to the unit glyph, eg '17xx' for '17score' Chinese is written as eg 1 h 6 t 4 as seperate characters.

Our number words go this way. Butterworth (The mathematical brain) notes that this is the most advanced form, since one is less likely to read two thousand and six as 20006 (ie 2000 6).

• True positional, first used in a division-system by the sumerians (of alternating 6, 10), zeros are recorded in leading and medial positions, eg 0 0 5 for 5". When used outside the sexigesimal context, units are attached, eg 0° 0' 5".

The mayan system with the column of 18 is purely a calendar system, the common count was in scores and scores of scores. Fractions were done in the greek fashion (ie ratio of numbers).

Zero, in its modern sense, was invented by the greeks around 600 AD. It followed the muslums to india, and returned by the same route. One notes that there are five different kinds of zero.

• Zero by itself. the egyptians had a symbol for an empty bag, even though no column or row zero,

• Leading zero: This is needed when the leading or most significant position carries meaning. Sumerian systems had this, because the first-referenced number is then divided to get other columns. 5 and 0 5 are different numbers, but 5 0 = 5 (where the columns stand for degree minute second)

• Trailing zero: These are useful in multiple-systems, where columns to the left depend on the right column. In fractions, these have no measure except to show precision, eg 5 0 0 is different to 5 0, but 5.0 0 is the same as 5., except to show more precise. Trailing zeros are not recorded in the sumerian system).

• Medial zeros: Zeros might be shown where the denomination is absent, even when units are used (Mayan system records, eg 1lb 0oz 2dr). Medial zeros are known in sumerian number systems. (See Neugebauer "The exact sciences in antiquity")

• Semimedial zero: None are recorded, but if as the alternating-digit systems go, let A=10, B=20, &c. A is 10, A7 is 17, A 0 is 600, and A 7 is 607. The semimedial zero is represented by the staggered column represented by dots in "A. .7"

Historical bases (being the repititions of columns in the abacus), include 10, 20, 40, 60, 80, 120. These arise from the two-row abacus, of 2/5, 4/5, 4/10, 6/10, 8/10, and 12/10. A 10/10 style in the vein of the sumerian system is also recorded, but this is not the precursor of the modern number system.

Modern decimal fractions derive from several inputs, the historical evidence is that of submultiples (where a count of 10 represents 1 in the next unit), since the earliest modern decimals have indicess written over them. However, the inspiration of this may well have been added fractions (eg 3 1/7 2/24 being 3+(1+(2/24)/7), as one sees eg 3 weeks, 1 day, 2 hours. In any case, the system is contrasted with the sumerian degree/minute/second notation.

By the way, i regularly use an alternating base (120) for calculations.

--Wendy.krieger (talk) 08:17, 26 February 2009 (UTC)

The lead says:

It is the most widely used numeral base

and someone added

[citation needed].

and I thought: Don't be ridiculous... but, thinking a bit more about it, I realized that the most widely used base IN NUMERICAL CALCULATIONS is binary, in the sense that most of the additions, multipliplications, etc. that are performed on any given day are done by computers, not by humans. So while we don't really need a source, we may need a qualification; something like:

It is the most widely used numeral base in human communications

... but I don't really like that either. Any good ideas?--Noe (talk) 06:48, 21 October 2009 (UTC)

The article claims "decimal fractions were first used ... by Arab mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century". That is incorrect. He was not the 1st person to use it.

According to the Cambridge University in England, decimal fractions were 1st developed and used by the Chinese in the 1st century BC, and then spread to the Middle East and then to Europe.

Source : Science and Civilization in China (Vol. 3) (Published by the Cambridge University Press)

Wikiwikidaddy (talk) 07:45, 30 October 2009 (UTC)

The decimal fractions as used in China did not make it to the west. Decimal numbers, with the use of zero derive from late greek, borrowed through the arabs to india and europe. The use of decimal fractions is modeled originally on the use of "second tenths", where a number had a superscript representing the order of division (eg writing 1234 over the digits 1 4 1 6 in pi= 3.1416.

The present decimal fractions are derived from the system of minutes and seconds, using 10, rather than 12 or 60 as the value of the minute.--Wendy.krieger (talk) 08:03, 30 October 2009 (UTC)

Decimal fractions are not the same thing as decimal numbers (and the use of zero). I have created another section below for that so as not to confuse the issue. As for decimal fractions (and also the section below), if you dispute the findings of the Cambridge University, you need to provide an argument backed up by clear evidence. Wikiwikidaddy (talk) 08:42, 30 October 2009 (UTC)

If no-one objects, I will update the main article with the corrections tomorrow. Wikiwikidaddy (talk) 03:50, 2 November 2009 (UTC)

We have a "list of recorded decimal writers" in this article:

• c. 3500–2500 BC Elamites of Iran possibly used early forms of decimal system.^[1][2]
• c. 2900 BC Egyptian hieroglyphs show counting in powers of 10 (1 million + 400,000 goats, etc.)—see Ifrah, below
• c. 2600 BC Indus Valley Civilization, earliest known physical use of decimal fractions in ancient weight system: 1/20, 1/10, 1/5, 1/2. See Ancient Indus Valley weights and measures
• c. 1300 BC Chinese writers show familiarity with the concept: for example, 547 is written "Five hundred plus four decades plus seven of days" on an inscription of an oracle bone^[3]
• c. 400 BC Pingala—develops the binary number system for Sanskrit prosody, with a clear mapping to the base-10 decimal system
• c. 250 BC Archimedes writes the Sand Reckoner, which takes decimal calculation up to 10^{80,000,000,000,000,000}
• c. 100–200 The Satkhandagama written in India—earliest use of decimal logarithms
• c. 476–550 Aryabhata—uses an alphabetic cipher system for numbers that used zero
• c. 598–670 Brahmagupta—explains the Hindu-Arabic numeral system (modern number system) which uses decimal integers, negative integers, and zero
• c. 780–850 Muḥammad ibn Mūsā al-Ḵwārizmī—first to expound on algorism outside India
• c. 920–980 Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi—earliest known direct mathematical treatment of decimal fractions.
• c. 1300–1500 The Kerala School in South India—decimal floating point numbers
• 1548/49–1620 Simon Stevin—author of De Thiende ("The Tenth")
• 1561–1613 Bartholemaeus Pitiscus—(possibly) decimal point notation.
• 1550–1617 John Napier—use of decimal logarithms as a computational tool
• 1765 Johann Heinrich Lambert—discusses (with few if any proofs) patterns in decimal expansions of rational numbers and notes a connection with Fermat's little theorem in the case of prime denominators
• 1800 Karl Friedrich Gauss—uses number theory to systematically explain patterns in recurring decimal expansions of rational numbers (e.g., the relation between period length of the recurring part and the denominator, which fractions with the same denominator have recurring decimal parts which are shifts of each other, like 1/7 and 2/7) and also poses questions which remain open to this day (e.g., a special case of Artin's conjecture on primitive roots: is 10 a generator modulo p for infinitely many primes p?).
• 1925 Louis Charles Karpinski—The History of Arithmetic^[4]
• 1959 Werner Buchholz—Fingers or Fists? (The Choice of Decimal or Binary Representation)^[5]
• 1974 Hermann Schmid—Decimal Computation^[6]
• 2000 Georges Ifrah—The Universal History of Numbers: From Prehistory to the Invention of the Computer^[7]
• 2003 Mike Cowlishaw—Decimal Floating-Point: Algorism for Computers^[8].

What is the point of this? It is not explained at all. At first, I assumed it was notable developments in the use of the Hindu-Arabic numeral system, but it also includes modern writers who discuss binary and related issues for computing. I think this section should be better motivated, focused and pared down. I've commented out most of the modern authors because I don't think that they belong here. Cheers, — sligocki (talk) 21:20, 30 October 2009 (UTC)

==================

Some of your points above are not backed up by evidence. Eg, the Indus Valley Civilization's use of measurement units that are fractions of our measurement units does not itself imply they used fractions. And more importantly, the use of fractions is not the same as the use of decimal fractions. Most advanced ancient civilisations used fractions. But there is no concrete evidence any used decimal fractions (as opposed to the common fractions) before the 14th century BC. Wikiwikidaddy (talk) 01:23, 31 October 2009 (UTC)

What are you talking about? I just copied this list from the page. I am saying that I think it is poorly constructed. Do you agree with me? Cheers, — sligocki (talk) 21:23, 1 November 2009 (UTC)

--- I see. My appologies. Thanks for the clarification. (And yes, I think you have a point) Wikiwikidaddy (talk) 03:36, 2 November 2009 (UTC)

Alright, I just got rid of it. If anyone wants to make a more appropriate list, it's copied here. Cheers, — sligocki (talk) 17:41, 3 November 2009 (UTC)

Simon Stevin's contribution to decimals is generally recognized to be the seminal one, see for example van der Waerden, or the St Andrews pair of articles which clearly relate to Stevin as a watershed. Is it reasonable to have all sorts of multicultural characters mentioned here, and leave out Stevin? Tkuvho (talk) 15:11, 21 February 2010 (UTC)

Your statement was incorrect. It appears he developed the basis for the modern notation, but he did not develop or "introduce" "the decimals we use today". — Arthur Rubin (talk) 15:19, 21 February 2010 (UTC)

Yes, his notation was different. I now see that my phrasing was misleading. At any rate he should be mentioned here. Tkuvho (talk) 15:26, 21 February 2010 (UTC)

See what I changed it to. I think the citation is still needed, but it's appropriate there. — Arthur Rubin (talk) 15:27, 21 February 2010 (UTC)

van der Waerden, B. L. (1985) A history of algebra. From al-Khwarizmi to Emmy Noether. Springer-Verlag, Berlin. Tkuvho (talk) 15:28, 21 February 2010 (UTC)

Is there actually a specific reason that almost the entire world uses the decimal system, i.e. is there a logically imperative reason for its popularity or is this simply arbitrary? Is there a scientfically valid difference in using another base system? —Preceding unsigned comment added by 217.85.239.236 (talk • contribs) 19:31, 22 February 2010

It is almost certainly because humans have ten fingers. A different base would work fine. Of course if you go too small, then your numbers get too long, and if you go too large, then you have to memorize too much for addition and multiplication, so there is a tradeoff. --Trovatore (talk) 20:54, 22 February 2010 (UTC)

The article claims "The modern number system originated in India". That is incorrect.

According to the Cambridge University, the decimal system (together with the digit zero) originated in China. The most conservative estimate for the use of the decimal system dates it to no later than the 14th century BC (although it is known to have been in use long before that).

Source (1) : Science and Civilization in China (Published by the Cambridge University Press)

Source (2) : Genius of China (by Robert Temple) (This book has won numerous major literary awards including ones from the American Library Association and the New York Academy of Sciences, and was translated by UNESCO into 43 different languages ).

Wikiwikidaddy (talk) 08:42, 30 October 2009 (UTC)

I have some serious issues with the 'Genius of China' by Robert Temple - this is an author who believes that extra-terrestrials had contact with early humans! I would like to see a more in depth discussion of these supposed inscriptions from the 14/13th century BC!

If no-one objects, I will update the main article with the corrections tomorrow. Wikiwikidaddy (talk) 03:50, 2 November 2009 (UTC)

The chinese system does not seem to have passed through india at all. We do not have any inheritance of the style of 5h2t3 for 523, this being a feature of chinese names. The number system, with its attendant zero, is derived by the Greeks, (using alphabetic '10' as zero), this was spread by the moslems to india and back to europe. We have other typical indian/arabic features such as placing 0 at the end of the digits. --Wendy.krieger (talk) 07:37, 24 February 2010 (UTC)

• The facts points to the contrary. In 1986 and 1986, Professor Lam Lay Yong of Singapore University studies the ancient Chinese mathematical work the Sun Zi Suanjing(The Mathematical Classic of Sun Zi) and compared its mutiplication, division method with islam mathematics works

by al-Uqlidisi, with a Latin tranlation of Musa al-Khwrizmi of 825, with works by Kushyar ibn Labban, and founnd that in these early islam mathematic works, the method of division using Hindu-Arabic numerals is indentical to the Chinese rod numeral method described in The Mathematical Classic of Sun Zi, to the finest detail, even the shifting of the numbers of multiplier from left to right by one position, was copied in toto in these early ISlam works. Even the expression of the remainder after division as fraction is identical to Sun Zi.

This is more mind boggling, given that the fact the rod numeral decimal system is a operational system by moving rods on counting board(actually on floor or table top), while the these islam works written more than 400 years after and based on WRITTEN calcuation, shared the exact procedures to the last minutes, some of these operation such as after divsion by one digit, must move the whole set of divisor numbers from left to right one position, which is whole un necessary and and cumbersome in a calculation system based on written symbols, one cannot just simply move the numbers around, like move counting rods on floor, but must involve re writting. Too much conincidence to explain away with independent development. Further, Dr Lam also pointed out the fact the before the advent of 0 in India, Indians used a blank space to represent a zero, which is extremely odd and un natural in a written system; while in rod calculus, a blank space in counting board (read counting table top) is the intrinsic of rod system, for example 3 minus 3 means take away 3 rods from 3 rods, naturally no more rods left on the board and left a blank. The blank in rod numerals in natural, the blank in written symbol is not intrinsic in Hindu Arab system.

Dr Lam believes, that the only logical explanation of these perplexing facts is that the Indian-Arab decimal had its origin in Chinese rod numeral system, which was in used in China much earlier than the earliest Indian record of decimal system. The Indian version was introduced to Islamic world by Musa al-Khwzizmi, the translated into Latin and transmitted to the west.

Propronents of Indian origin must answer the following facts, why an empty space in their early decimal system ? Why translated Indian system as appeared in several Islam works show such striking similarity up to the last minute with Sun Zi'w work ?

It is not difficult to explain the transmission of Chinese rod numeral system (the only methd of calculation used by the Chinese, until the advent of abacus) from China to India. From 266-to 399, there were on record, Zhu Fahu, Kang Falang, Yu falan, Zhu Niafo, Hei Chang, Hui Bian, Zi Faling, Fa Jin, anf Fa Xian travelled to India.

I believe Cambridge University and Rober Temple is right, the decimal system was originated in China, not India --70.50.200.249 (talk) 23:51, 8 April 2010 (UTC).

Joseph Needham, Robert Temple never claimed that the written 0 was invented in China, probably invented in eastern region of India close the southern China culture, or in Cambodia. Chinese carried out complex mathematical calculation with counting rods, they don't need a special 0 symbol, not until 13th century, 0 symbol appeared. It must be emphasiz here, the appearance of written 0 does not implied conceptual invention, as Needham pointed out, the Brahmi numerals which the Hindu- Arab system supposed to derived from, was no improvement from the Greek and Hebrew numeral system.--70.50.200.249 (talk) 00:02, 9 April 2010 (UTC).

• • "Because of ten fingers" has being the common anwser to why decimal system and not octal hexa system etc. IMO, "10 fingers" is an answer, but not a good one, because it does not answer the question why Greek or Brahmi decimal numerals used much more than ten symbols.

There is good answer as to why the Chinese counting rods of the Spring and Autumn period stop at 9, and no more then nine symbols.

Because, the ancient Chinese had "Worship of Nine" culture, stemmed from the Book of Chang. Ancient Chinese classified even numbers such as 1,3,5,7,9 as Yang, and 2,4,6,8 as Ying, 9 being the highest of the Yang number, was considered the supreme number, thus an emperor was called "Nine five supremacy", correspond to the the first Hexagram of I Ching, the "Heaven, Yang, and Male" Hexagram, which, each bar was called a Nine, the fifth bar called a Nine-Five, corresponding to "Flying dragon on the Heaven"-- the emperor. Do you think a court mathematician who held the highest math post in a kingom dared to get ahead of "nine" and higher than the emperor ? Thus the counting rod must stop at nine and no more.

The worship of Nine casted a deep mark on history of Chinese mathematic:

• The Chinese multiplication table begain with 9x9, and ended at 1x1
• the most important mathematic work in China, which influence the development of mathematics in China for more than a millenium, was titled "The Nine Chapters of Mathematics".---Gisling (talk) 02:13, 11 April 2010 (UTC).

Recently a priority claim for chinese mathematics was added to this page, which seemed to be properly sourced in a publication in a respectable journal (as well as a respectful mathscinet review). The changes were reverted together with some argumentative material. This should probably be discussed here. My own feeling is that both indian contribution and the chinese contribution should be discussed, preferably avoiding dramatic priority claims, but this also shouuld be discussed. Tkuvho (talk) 12:05, 8 April 2010 (UTC)

If I recall correctly, the Chinese section replaced the Indian section. If both sections are properly sourced, even if they disagree, they both should be in the article. — Arthur Rubin (talk) 13:22, 8 April 2010 (UTC)

I second Arthur's opinion. Both sections should be toned down so as to avoid unnecessary controversy. Tkuvho (talk) 13:51, 8 April 2010 (UTC)

I believe you are referring to my revert. I agree with you guys, it is good to have balanced coverage, but most of what was added was clearly not encyclopedic. Feel free to add back in encyclopedic content. Cheers, — sligocki (talk) 00:47, 9 April 2010 (UTC)

Should this be focused on positional decimal systems, or all decimal systems? Roman numerals are also a decimal system, but it is not positional. I have the impression some of the new material in the Chinese section is not referring to positional decimal notation. Tkuvho (talk) 07:59, 9 April 2010 (UTC)

It must be emphsized that

1) the title of this article is Decimal, not "positional decimal" 2) Positional decimal is a subset of decimal, in China, non positional decimal appeared first, than evolved into positional. The counting rod was positional from the start. 3) To full understanding how non positional decimal evolved into positional decimal, one must examine the step by step history, it is no use just pointing to a piece of artifact and declared it to be a smoking gun evidence. --Gisling (talk) 02:22, 12 April 2010 (UTC).

Western historians cited immediately after the chinese section seem to dispute both (1) the claim that chinese decimals were positional, and (2) the early dating in the "spring and autumn" period, which falls at least 400 years before what Needham is willing to credit. Someone more knowledgeable than me in chinese history needs to take a look at this. Tkuvho (talk) 08:39, 9 April 2010 (UTC)

• • Must emphasize again, don't make the mistake of looking only at WRITTEN DECIMAL, and igore the decimal device. In China, there was two

parallel lines of decimal, written Chinese decimal was not decimal, counting rod is. A good analogy is our daily written numeral is not binary, but the computer we us is. Counting rod was the computer of ancient China, neglect this is a big mistake. Put it in other words, the

Chinese used positional decimal computing device a millenium before any other civiliztion ---Gisling (talk) 02:22, 12 April 2010 (UTC)

Actually, I notice that Needham is talking about decimal fractions, not decimals. Tkuvho (talk) 08:59, 9 April 2010 (UTC)

Gisling wrote: "Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics." I did not classify either of them as "official chinese line". When speaking of the "official chinese line", I was referring to reliance on the great chinese encyclopedia, whose objectivity I think is questionable. Work by Wu, Shen, and Li published in reliable western periodicals would be just as welcome as work of Lam Lay Yong. A critical attitude toward the chinese encyclopedia does not bring politics into the discussion, as you suggest. On the contrary, such a critical attitude is an effort to keep politics out of the discussion. We all know who made a laughing stock of themselves in pursuing chinese priority for the proof of the Poincare conjecture. What is not sufficiently realized is that, were it not for the efforts of single individuals such as Sylvia Nasar, the Poincare conjecture page would currently present a 450 explanation of how the chinese proved it. I appreciate your willingness to rely on western sources in documenting decimals and positional decimals. Given that distinguished scholars such as Joseph Dauben worked in the history of chinese mathematics, this should not prove an impossible task, and I appreciate your putting in the time. Tkuvho (talk) 07:46, 12 April 2010 (UTC)

I just noticed the following additional comment by Gisling, inserted in the middle of my edit here: "Counting rod was the computer of ancient China, neglect this is a big mistake. Put it in other words, the Chinese used positional decimal computing device a millenium before any other civiliztion". This is a fact that should be definitely included if it can be properly sourced. Again, I have no problem with chinese priority, so long as it is documented in reliable western sources. Tkuvho (talk) 08:50, 12 April 2010 (UTC)

The current series of edits by Gisling started by quoting a paper by Lam Lay Yong, in a reputable western journal "Archive for History of Exact Sciences". Since then, Gisling's additions have been dominated by the official chinese line. Thus, the typical "Footnote 6" currently states: "This view was adopted by the editorial board headed by Wu wen Tsun of Chinese Academy of Science for The Grand Series of History of Chinese Mathematics" (the editor appears under Wu Wenjun). Now the official chinese line may not be consistent with Western scholarship, any more than the Great Soviet Encyclopedia on the issue of priority of invention of non-Euclidean geometry. I would suggest moving all material not sourced in Western sources, to the talkpage for discission. Tkuvho (talk) 11:45, 11 April 2010 (UTC)

• Drawing an artificial line between the West, China, Soviet is contrary to the charter of wikipedia, That would set a bad example of making wikipedia into a politicpedia.

Wu Wenjun, Shen Kangshen, Li Di are all well respected historians in Chinese mathematics, ASAIK, none them are communists, where comes this label "Chinese lines ", just is is unreasonable to label books by Cambridge U as "Capitalisism line, imperialist line" .Shen Kangshen published book with Cambridge University Press, the historian of math is a small world, Jean Claude Martzloff, K Chemla, U. Libbrecht, Lam Lay Yong met in international conferences in China and abroad every year,every one knows other one's work, and Martzloff, Librecht, all has Chinese name, in short, they are like a family. Your classificaion of Wu, Shen, Li as "offical Chinese line" will be a laughing stock for international scholars on history of Chinese mathematics.

I absolutely oppose Western Central Point of View, "western scholarship" is pure prejudice.

Once politics enters wikipedia, it will be doomed --Gisling (talk) 01:59, 12 April 2010 (UTC).

In considering the fact that most reader of the en.wikipedia do not read Chinese, I shall try my best to replace a part of the Chinese references with English reference, just for the convenience of readers of en.wiki, not a matter of principle--Gisling (talk) 04:06, 12 April 2010 (UTC).

I have move most materials from Chinese language sources to talk page, leaving only one citation on archeological evidences. Now in this paragraph, the citations are mostly from English literatures by Joseph Needham, Robert Temple, Lam Lay Yong and Yoshio Mikami--Gisling (talk) 10:42, 12 April 2010 (UTC).

(edit conflict) The section needs to be reduced in size to a one or two paragraphs and cleaned up. If there is enough source material, this can be forked out to a new article, as we have with the Hindu-Arabic numeral system, but at present the focus is grossly out of proportion to the rest of the history section and the focus of the article. Also, sources with a broader diversity of opinion need to be brought in, since all of the current sources appear specifically selected to build the case that the Chinese originated the positional number system. Sławomir Biały (talk) 11:09, 12 April 2010 (UTC)

Suan shu shu. A book on numbers and computations. Translated from the Chinese and with commentary by Joseph W. Dauben. Arch. Hist. Exact Sci. 62 (2008), no. 2, 91--178.

This text gives a lot of information on chinese mathematics from 2200 years ago. I have not found anything about decimals, though. Will keep looking. Tkuvho (talk) 09:54, 12 April 2010 (UTC)

• It appears that the Suan shu shu used decimal arithematic procedures involving decimal fractions, such as "田二十八万八千七百五十顷" (land 288750 acre) "二千一十六分之百六十二，约之，百一十二份之九“ （ 162/2016 = 9/112）. Apparently the computation in Suan shu shu was carried out with counting rods, it used the terminology "place 2, place 4, place 8, place 16, place 32", for placing counting rods on the floor--Gisling (talk) 11:26, 12 April 2010 (UTC).

Do the numbers 162 and 2016 appear in positional notation here? Tkuvho (talk) 11:42, 12 April 2010 (UTC)

• • The numbers in Shuan shu shu were written in Chinese ideograms. As always, the Chinese written numerals are decimal, not positional. The positional decimal notation lived only in computing devices as a device language, ie, counting rods and abacus. This is probaby one interesting distinction of Chinese math vs math in other ancient civilization- she had a device language in addition to written language. The Chinese never carried out any calculation on paper, not until the Arabic notation was imported to China in Ming dynasty, then become more popular in Qing dynasty--Gisling (talk) 12:14, 12 April 2010 (UTC).

In this article "The modern numeral system format, known as the Hindu-Arabic numeral system, originated in Indian mathematics[15] by the 9th century."

but in Hindu–Arabic numeral system

"The development of the positional decimal system takes its origins in Indian mathematics during the Gupta period. Around 500 CE the astronomer Aryabhata uses the word kha ("emptiness") to mark "zero" in tabular arrangements of digits. "

in Indian mathematics

"The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE.[52] A copper plate from Gujarat, India mentions the date 595 CE, written in a decimal place value notation, although there is some doubt as to the authenticity of the plate.[52] Decimal numerals recording the years 683 CE have also been found in stone inscriptions in Indonesia and Cambodia, where Indian cultural influence was substantial.[52]"

any one who knows more about Indian mathematics, please fix this inconsistency. Please provide more concrete evidence, such as how the ancient Indians carried out calculation ? On paper ? with abacus etc etc, dates ?--Gisling (talk) 13:18, 12 April 2010 (UTC).

This book gives detailed number systems, with plenty of examples of digits from various epochs.

The previous decimal system in places like china, is that of number exponent pairs, eg 9 C 2 X 5 for 925 (ie 9 hundred 2 ten 5). Since the chinese use characters as words, this could as equally be the written form.

The forms given for india, show large variations in the digits 1-9, but 0 is consistantly shown in two forms: as an open circle, and as a point like a modern bullet-point. This suggests that 0 was borrowed into Indian culture. The chinese form is an open circle, but this is entirely uncharacteristic of the caligraphy of the time, suggests that China borrows it from the Indians.

For the Arabs, that the entire alphabet was reworked from traditional Semetic order to a form more accomidating of the greek alphabet, largely to allow the greek numbers to be used without modification. The order of borrowing is to use greek letters as numbers, then arabic numbers, then hindoo numbers.

The suggested migration is then from the Muslims to the Indians to the Chinese.

The greeks already had iota representing both 10, and in a different system, 0. This system existed around C4 (ie late 300's). This is what i consider to be the source of the modern decimal system.

One notes with Butterworth (The mathematical brain), that the use of number + weight (eg 9c2x5) is less prone to give errors, and a more advanced system than long digit strings (eg 925). One particular error avoided is writing '1008' for 108, or 1c8, in the sense of 1 00 (hundred) and 8 ie 1008. --Wendy.krieger (talk) 07:42, 13 April 2010 (UTC)

Very interesting. Ifrah should be discussed more fully on the page itself. As for Butterworth, there does not seem to be any reference on the page itself. Please elaborate there. Tkuvho (talk) 14:53, 13 April 2010 (UTC)

I did a good deal of research into number systems with view in reviving base 120 for general use. Most parts of number, weights and measures and number theory was covered.

Brian Butterworth, 1998 "The Mathematical Brain". This deals with evidence on how the mind deals with number, eg from linguistic and from clinical approaches. "clinical" here means looking at what people with some brain damage deals with numbers. The account of things like 1 00 8 (one hundred eight) is from here.

Multiplication and Division are different processes, handled by different parts of the brain. This is why, for example, different bases have been used for these. Division is handled by different parts of the brain by different individuals, which is why we see different processes.

The extent of digits usually represents 'animal counting'. Grouping into higher orders is essentially a human trait. One also notes the transition from ordinal count (second finger on the third hand) to cardinal count (two hands two fingers), proceeds large numbers.

Of the ancient methods of reckoning, most are still in use. Here is a rough list, including the form and (calculation devices).

• × Token Denominations eg symbol for powers of 10, eg Egyptian system. I, X, C, M. out of use?

• × Coin denomination, eg symbols for intermediates (eg 50 = L, 5 = V) = still used for coinage.

• × digit + denomination eg 5 C 2 X 9 for 529: eg chinese numbers.

• × digit-denomination combined (eg alphabetic numbers, demotic numbers, names like 'fifty' for five tig).

• × raw digit expression, eg five two three (in use in places where the columns are prestated, eg navigation).

• ÷ Egyptian fractions = sum of recriprocals (Tables of 2/n) - currently out of use

• ÷ Sumerian fractions = division of units to avoid division (Tables of inverses, Multiplication reckoners) - fractions still used, methods out of use.

• ÷ Greek fractions = ratio of integers (Euler's algorithm for gcd) - Still in use. [Mayans used this system]

• ÷ Roman fractions = measure by weight (where 1 = ft = lb) - still in use (24 carats = 1 solidus, 6 solidus = 1 oz), also use of things like dollars of radiation where one dollar = critical level.

• ÷ Latin fractions = added fractions (eg 4 5/10 1/3) = 4+(5+1/3)/10. Still in use, eg use of fractions after decimals.

• ÷ Radix fractions = decimals.

• ÷ "Continued fractions" are not in general use to express fractions.

--Wendy.krieger (talk) 08:22, 15 April 2010 (UTC)

This sounds fascinating if somewhat telegraphic (I was not able to follow some of the points). Could you incorporate some of the main points here? Tkuvho (talk) 11:18, 15 April 2010 (UTC)

I've just removed the following reference from this page:

"Current reseach into Chinese mathematics has demonstrated that much of the Indo-Arabic number system's foundation might have been built in ancient China" Zorn, Christian, Cultural and Geopolitical Influences on the Development of Mathematics, August,2001, Ohio Statue University [1]

If you look at the date, it was clearly written as a term paper when that author was an undergraduate.

Still worth to read, as he is now an assistant prof in Math department of OSU, further his article cited many valuable references such as Ifrah, Martzloff

[2]--Gisling (talk) 21:37, 21 April 2010 (UTC)

It does have some interesting material and references, no doubt about that; but it was clearly not suitable to be cited here as a reference.

All the best. (And my apologies for not signing my original comment). Syncategoremata (talk) 21:55, 21 April 2010 (UTC)

Just to clarify that. I meant Chinese shí (=10), of course, in my edit summary. Gun Powder Ma (talk) 22:01, 21 April 2010 (UTC)

Gun Powder Ma (talk · contribs) has been reinserting material which I consider inappropriate into the article. Although he/she was the first to Boldly insert the material, I'm willing to be the first to discuss it. My specific concerns on the latest reinsertion:

1. "Greek Number Systems" is inaccessible at the moment, but appears to be a news group posting. It has no reliability without there being a web site editor or the author having credibility.
2. "A Brief History of Zero" appears to be a blog. If it were to be reliable, it would need to be a courtesy copy, or the author must be a recognized expert.
3. The relevance of current Chinese numerals being a non-positional decimal needs to be sourced.

— Arthur Rubin (talk) 22:19, 21 April 2010 (UTC)

1. Earlier this day, it was online, but it is the best source on ancient mathematics online.
2. I will look for a further source.
3. Nope, wrong. It was already sourced, by linking to Chinese numerals. It is a self-evident fact that the modern Chinese numeral system is not positional. 10 (shí) and 100 (yi bai), for example, are non-positional. If you refuse to spend 120 s on looking yourself into the matter, I fear you will need to spend 120 min here, arguing from a lost position. As for the relevance, the whole section on the Chinese positional system seems to much out of scope, since this article is about decimal numerals, and only ancillary on the positional system. Gun Powder Ma (talk) 22:40, 21 April 2010 (UTC)

• • " modern Chinese numeral system is not positional" is misleading, as Chinese written numeral system from antiquity to now has NEVER being positional, the Chinese written numeral was used for documentation purpose, never a calculation media. Chinese used counting rods numeral and abacus for positional decimal calculation--Gisling (talk) 07:27, 22 April 2010 (UTC).

A former French school teacher, in order to answer pupil's question, determined to become Indiana Jones of math, wrote a popular book on numbers.--Gisling (talk) 08:07, 1 May 2010 (UTC).

Uh, what, you're questioning Ifrah? From what I've seen, my general impression is that he's one of the foremost living historians of mathematics. Shreevatsa (talk) 08:38, 1 May 2010 (UTC)

• • Not by real math historians:

“Historians of mathematics in particular have voiced strong reservations about Ifrah’s pronouncements on the history of number systems... In 1995 a group of five experts in France agreed it was necessary to confront the popularity Ifrah’s work was being accorded and to point out explicitly his numerous misreadings, misinterpretations, and pure fabrications....Lévy explains that he and his colleagues felt an obligation to “rectify [Ifrah’s] deceptive, confused,even muddle-headed views.” They felt compelled to do so he says because of Ifrah’s relentless habit of presenting conclusions that are “often debatable,generally weak, and at times wholly imaginary,”as if they were “historically valid theses”

Dauben review of Ifrah' book]--Gisling (talk) 10:43, 1 May 2010 (UTC).

I've removed the ad hominem comment on Ifrah from this article but attempted to appropriately qualify the claims taken from him. I've also added the critical AMS review of his works to his page here on Wikipedia.

Many thanks for the link to those reviews, by the way: I'd checked various reviews of his works before (from scholarly journals) but they had been generally positive, if not entirely accepting of his work. None of them had dealt with his works in that level of detail though.

All the best. –Syncategoremata (talk) 12:33, 1 May 2010 (UTC)

• Ifrah's book is interesting and fascinating, with lot of pictures and diagram. I think if his

statements of supported by references than it should be considered reliable, otherwise, should be deemed his "orginal research" and used with caution. --Gisling (talk) 13:12, 1 May 2010 (UTC).

Good to know, thanks. Shreevatsa (talk) 16:05, 1 May 2010 (UTC)

That's inappropriate. If his work is seriously criticized, it shouldn't be used as a reference without including that criticism. — Arthur Rubin (talk) 16:21, 1 May 2010 (UTC)

I've included the reference to the criticism from his article; as it's a review of the reference we're using, it seems appropriate. — Arthur Rubin (talk) 17:07, 1 May 2010 (UTC)

It would be better to use another reference, instead of citing one book and then criticizing it. After all, I don't think any of the claims made are really specific to Ifrah. Shreevatsa (talk) 17:30, 1 May 2010 (UTC)

It's not my field of study, so I wouldn't know where to look for a reliable source. The problem seems to be there are few sources which claim that early a "discovery"/invention, and that's the point being emphasized. If I had a copy of the reviews (well, my father probably does, so I'll see if I can get copies), and if one of the reviews specifically comments on that claim, it probably should be listed in the paragraph. Just saying that the reference is disputed isn't great, as we don't know whether those specific claims are disputed. — Arthur Rubin (talk) 07:39, 2 May 2010 (UTC)

I second Arthur on this. Just because someone wants to be an Indiana Jones does not make him a reliable historian. Joseph Dauben is a serious historian of Chinese mathematics, and I would take his evaluation over a popular book anytime. What does he think of Ifrah's specific claims? Tkuvho (talk) 11:20, 2 May 2010 (UTC)

• • One thing bothers me: at the end of the Dauben's review, he pointed the the unusually fine print disclaimer by John Wiley: "It is sold with the understanding that the publisher is not engaged in providing professional services. If professional advice or other expert assistance is required, the service of a competent professional should be sought". I checked my other Wiley books, none has such kind of disclaimer, which is rather odd.

A lot of statements in Ifrah's book were stated without reference. This makes citing his book as reference problematic. For example the statement about|pañchabhyah khalu shûnyebhyah param dve sapta châmbaram ekam trîni cha rûpam cha" has no reference. A search with google leads to Ifrah only, looks like his own opinion, but then, is he an ancient Indian language expert ? How reliable is his statement ?, Given the fact that he stated that eka，pitamaha,adi,tanu……all meant "one" ，dvi,ashvin,Yama, yamala, netra,bahu,guophau, paksha all meant "two"...|nava,anka,graha,chhidra meant nine, shunya,binda,kha,ambraha...meant zero . All these makes people confuse.

--Gisling (talk) 01:01, 5 May 2010 (UTC).

I don't know if the statement actually appears in the work, but his translation is accurate (and presumably he had the help of someone else) (although shûnya means just "zero" these days rather than "void", and "rūpam" can have many meanings, the one given is reasonable). About the other statement, he's essentially right — to understand why many words could stand for the same number, see Bhūtasaṃkhyā system. (For example, "ashvin" is two because there were two of them, similarly 'netra', 'bahu' (eyes, shoulders), graha (nine "planets"), etc.

The broader point, though, remains. It is strange that there are no other Google results, but then again, not everything is on the internet, and as Filozoat or someone in the AMS review points out, the history of Indian mathematics is still curiously under-researched, so it's possible Ifrah dug up the quote himself. (The Wikipedia article on Lokavibhaga cites a 1992 book by Crump, in which such a claim does appear (again without reference!). Shreevatsa (talk) 03:11, 5 May 2010 (UTC)

Imagine someone with two digits on each hand developing their own numerical system. This system goes 1, 2, 3, 10, 11, so on and so forth... Now imagine one of us were to meet this person in a neutral location. We observe that there is a cluster of rocks on the ground. We count all of the rocks using the fingers (excluding our thumb) on one of our hands. This special someone counts the rocks using their numerical system. They conclude that there are 10 rocks in this cluster. You of course make note of this fact and exclaim that this person must be using base 4, and express your preferred usage of base 10. They are confused, because they are using base 10, and base 4 doesn't make sense to them. All articles on Wikipedia regarding numerical systems must therefore make note of the fact that the naming system for any base is itself based upon base 10. 98.218.122.127 (talk) 11:19, 23 May 2010 (UTC)

What you seem to be pointing out is that the particular digits being used are only conventional. What we really mean by saying "base 4" is that we use base "number of corners in a square". However, having to say "number of corners in a square" instead of 4 may be awkward. Tkuvho (talk) 11:29, 23 May 2010 (UTC)

The normal means of expressing bases is to use the conventional base that the reader would expect. When there are several bases in use (eg old germanic), one writes in the form appropriate for large numbers (eg 'six hundred teentywise', that is 6 00, where 1,00 is ten×ten. I use several bases myself, see, eg http://www.os2fan2.com/gloss/index.html , but differentiate the numbers by postfix (twe: for 120, dec: for 10). <--Wendy.krieger (talk) 07:34, 25 May 2010 (UTC)small>—Preceding unsigned comment added by Wendy.krieger (talk • contribs) 07:32, 25 May 2010 (UTC)

The following reference "Azar, Beth (1999). "English words may hinder math skills development". American Psychology Association Monitor 30 (4). http://www.apa.org/monitor/apr99/english.html." links to an empty page. I did not edit the article but I thought you should be aware. Also, why isn't there more mention in the lead for this article about a connection (or lack of connection) between the assumption that our pre-homosapien/homosapien species having ten fingers was THE decider for base 10 being what we use everywhere today, maybe even coded in our genes (if there was a gene that made the understanding of base 10 easier, and also if an understanding of base 10 has been natural selection factor for long enough)? Unsigned intentionally. —Preceding unsigned comment added by 211.29.174.138 (talk) 17:29, 31 August 2010 (UTC) (Autosigned by SineBot)

The introduction indicates that mathematics education uses the word "decimal" to refer specifically to a decimal fraction as described later. This indicates that teachers and students do not use the word "decimal" for irrational numbers or numbers with infinitely repeating decimal expansions. This is ludicrous. Most students and teachers use the word "decimal" to discuss numbers that are not integers, refusing to acknowledge the integers as decimals. If no objections, I will edit the article to read, “In some contexts, especially mathematics education, the term decimal can refer specifically non-integer numbers. In such a case, the number 1.234234234... is called a decimal while the number 1234 is not. ” I'm not too happy with the example, but it is certainly better than the rubbish that was there before. Clifsportland (talk) 18:59, 26 August 2010 (UTC)

As there were no objections I made the specified edit. Clifsportland (talk) 21:44, 6 December 2010 (UTC)

I've made two changes. First, there was a statement that "It is the most widely used numeral system, perhaps because a human usually has four fingers and a thumb on each hand, giving a total of ten digits on both hands." The proper preposition is "over", not "on". "On" creates an ambiguity as to whether it means that each hand has a total of 10 fingers, or together have 10 fingers.

Also, there was a statement that + means plus and - means minus. When it comes to sign, that is WRONG. The signs are positive and negative, not plus and minus.

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Decimal is the number system humans use because of the fact that we have ten fingers.

I heard that some cultures prefered to use the hexadecimal system because they didn't count their fingers on their hands. But instead, they counted with one hand using one thumb to touch on the finger tips and the bends at their finger joints. (There are 16 points on each human hand, hence a hexidecimal system.) However, the decimal system became so wide spread internationally that it dominates now.

I heard about this over twenty years ago from my high school teacher. I don't know his source of this information. I am wondering if any wikipedians out there can confirm this.

If the counting finger-joints technique were more prevailing than counting fingers, human society could have adopted the hexadecimal system which is much better compatible with binary computers nowadays.

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The ancient Mayan civilization used base 20 in their numbering system. Their numeric symbols denote values from 0 to 19. (source: http://www.eecis.udel.edu/~mills/maya.htm)

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Avoid fallacies in arguments. Just because the people that use decimal do so because they have 10 fingers doesn't mean that all humans use decimal. Nor does it invalidate any of these base 16 or base 20 systems. The article should point out that not all people use decimal (and I will edit it). --drj

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I don't think there are any societies that used base 16 though. The highschool teachers story seems suspect. Base 20 is of course fingers and toes. But where does base 12 come from? --AxelBoldt

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12 presumably comes from months of the year. Many calendars have 12 months in a year (not just because it is nearly the number of lunar months in a year). Imagine you are an early geek into factors and astronomy. Observe: 360 days in a year, aha! that factorises easily with nice factors like 12, 60, 24, etc. The base 16 claim seems very dubious to me. Fingers and toes didn't occur to me though it is plausible. --drj.

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I think the 12, 24, 60 business came from the Babylonians/Persians? Somewhere that direction and long before Greece. --rmhermen I said "geek" not "greek"! Bablylonians/Mesopotamia is the generally agreed source I believe. --drj

The babylonian number system was base 60 according to Math historian, David M. Burton. He suprisigingly doesn't have a wikipedia page. Clifsportland (talk) 18:59, 26 August 2010 (UTC)

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Are roman numerals a number system? What is the base?

In Wikipedia, this is now called a numeral system -R. S. Shaw.

It's a number system, but not a positional one, so it doesn't have a base. --AxelBoldt

So perhaps the article on number systems should mention it?

In Wikipedia, this is now called a numeral system -R. S. Shaw.

Yes it should. --AxelBoldt

This page still states that the Roman numeral system is a base ten system. How should we remedy this? Clifsportland (talk) 18:59, 26 August 2010 (UTC)

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In the US weighing system, one pound = 16 ounces. In Chinese weighing system, one catty = 16 taels. Though they are not number systems, but at least it give some hints why the number 16 is involved in measurements universally. In any systems that use division, any power of 2 is a good candidate for convenience sake. For example, a gallon = 4 quarts = 8 pints = 128 fluid ounces = 1024 fluid drams etc.

One pound is also 16 ounces in the Imperial system from which the US one is derived, although (1) the Imperial pint is now 20 fluid ounces rather than 16, obscuring the (former) relationship between "pound" and "pint", and (2) for some reason the two "fluid ounces" are slightly different (the fluid ounce used to be that amount of pure water which weighed 1oz. at 70°F, just as today one definition of "kilogram" is the weight of 1 litre of pure water at 4°C). Thus a gallon of water weighs (about) 8Lb. in the US and 10lb. in Britain. -- 217.171.129.68 (talk) 22:35, 29 March 2008 (UTC)

Looks like human are attracted to the power of 2 and astronmonical periods and our fingers and toes.

A old British pound = 20 shillings

one old shilling = 12 pences

"Pence" is already plural (one of the plurals of "penny", the other of course being "pennies"), hence there's no such word as "pences". Incidentally, one penny nowadays (1p — in the few years after 1972, called "one new penny" to distinguish it from the previous penny) == 2.4 (old, pre-1972) pence (2.4d -- d for "denarius", anthough as noted there were 12 to the next unit, not 10 as the name implies). — 217.171.129.68 (talk) 22:35, 29 March 2008 (UTC)

20 and 12 can still be explained, but 1 mile = 1760 yards??? how did they come up with that number?

The roman cadasteral system is based on units of 120 or 240 feet [120 = actus], ultimately getting to 4800 ft. The itenitary mile is 1000 paces of 5 feet. In England, the mile was divided into 8 furlongs, each of 40 rods, the size of the rod varying according to the productivity of the country. The value adopted in a statue, wishing to state 5 miles, stated that the rod was 5 1/2 yards. Values vary from 10 to 24 feet for the rod.

There is evidence of a foot of 1.1 imperial feet, or 13.2 BI inches, which would make the corresponding mile some 4800 feet, in the roman practice. This mile and a shorter foot gives the required 5280 feet, or 1760 yds. --Wendy.krieger (talk) 08:30, 24 October 2009 (UTC)

Have you heard the story about how the butt size of the Roman horses decided the rail guage in the current US railroad system?

Railway gauge is set by the flanges of the wheels, which gives 4' 8 1/2". The Roman road were set with tracks at five foot centres. --Wendy.krieger (talk) 08:30, 24 October 2009 (UTC)

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In decimal counting, the Fibonacci numbers repeat the sequence of the last digit over a period of 60. Every other numeral system with base less than 14, repeats in less than half of this (often 24).

Base   Period of last digit of Fibonnacci Numbers
  2      3
  3      8
  4      6
  5     20
  6     24  (last two digits too)
  7     16
  8     12
  9     24
 10     60  (unusually big)
 11     10
 12     24  (last two digits too)
 13     28
 14     48

Karl Palmen

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I realize I am jumping to this without most of your comments. The statement is slightly misleading. I won't change it until I think of a way of wording the correction. It just happens that everybody uses arabic numbers when they write english so it is easier to convert all numbers to that system which happens to based on base 10. For example you could use base 60 for time, but the symbols are not universally recognized and you can easily flip from base ten to base 60 when talking about seconds and minutes. I am certain there are languages that use another base or consider it significant. Look at binary. Still base 10 is huge compared to it.Tempust (talk) 05:28, 24 February 2010 (UTC)

This article does not make it clear whether it is about the decimal aspect of the current world system, or the positional aspect. It says that our system is the one of two decimal positional systems. But then it compares non decimal systems to the system only discussing their base. What is truly needed is a grid of articlesh that looks like this, having an introductary article for decimal systems, binary systems, dodecimal, binary, vigesimal and sexigesimal systems, as well as an introduction for each of the ways of denoting the powers, positional, different symbols.. &c. However, as a start, the following might make sense:

an article on systems that use a different symbol to show how many, but use positions for powers -can be based on this article after a title change, and moving some stuff around -will also contain mention of common binary notation, and its dervitives (hex &c) -will also discuss all the different notations for the decimal system of this type, arab, western, gujarati, &c -base sixty fractions

an article about systems that have a different symbol for each amount in each order such as greek, hebrew, older arabic one -(abjad systems???)

an article about systems that have a different symbol for each power of the base, but write it multiple times in order to show amount -decimal ones: Roman, Egyptian, that other greek one that looks like hang man -sexigesimal ones: Sumerian, babylonian

an article about systems that use positions to show order and use accumalation of the symbols to show amound -sexigesimal: later babylonian -vigesimal: maya (the above two both use alternating symbol sets for the two factors of their base, so are not really pure)

Once this framework is done, there are probably lots of main articles that can be pointed to. —Preceding unsigned comment added by Alexwebjitsu (talk • contribs) 03:43, 18 February 2008 (UTC)

Decimals (decimal place) - see wikitonary

Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar fraction, this is done with the recent divisions of the troy ounce, which has three places of decimals, followed by a trinary place.

The use of ordinals to designate repeated fractions is seen in sexigesimal (second and third minutes, Newton goes as far as vi and vii), decimal (see, eg tenth-metre), duodecimal. Just as counting up is remainders by division by 10, so is fractions made by multiples of 10 and 'carry'. A method to convert this to another base is to carry out exactly this equation, eg the duodecimal of 0.14 becomes (by multiplying the fractions by 12) 1.68, 8.16, 1.92, 11.04, ... the integer parts become the duodecimal fractions: 0.1 8 1 11 .... --Wendy.krieger (talk) 08:14, 25 December 2010 (UTC)

I tidied up some fiddly mechanical bits in the first half of the article, but I had to leave the "History" section alone. This section has a great many issues; I think it needs to be extensively rewritten, but I lack the background knowledge (Chinese history, counting rods, abaci) to do so myself. Any thoughts? --Majestic-chimp (talk) 23:40, 31 December 2010 (UTC)

A good measure of the talk seems to be given over to discussing the nature of zero in modern usage, and the origin of the modern digital number system. This has nothing to do with decimal.

Zero, in its modern use, was used by the mayans in base 20. The Sumerian fraction system, used zero in leading and medial positions, eg 0 0 1 = 1 second, and 1 0 6 for 1h 6s, but not trailing positions (1 0 and 1 are identical to one). However, one can use a decimal system without using a zero, just as one can use such without a decimal point.

The modern western digits are indeed of indian origin, the etymology of zero (from 'sunna = empty'), suggests this too. The arabs were the ones that the Europeans borrowed it from, and the Chinese seemed to have borrowed the European scheme, making their traditional runes similar to names for these numbers, eg 'five ty six' but '56'.

Of course, 'base 10' is not the only historically relative base: one has many examples of 'base 100', that is, alternation of the base number over two places (ie 6-10 or 4-10 or 8-10 or 2-10 or 4-5 etc), by having the units row and the tens-row at different values. Even the examples of the chinese stick-numbers are 2-5, reflect the abacus they inherited from the romans.

And in this sense, "decimal" is not a particular creation that is carried from place to place, but something that arises freely in different places. Suggesting otherwise is to suggest the mayans and the celts (with histories of base 20), derive from a common pan-atlantic source, such as atlantis.

--Wendy.krieger (talk) 07:46, 25 May 2010 (UTC)

I think you have misunderstood the debate. I don't think any of the Chinese are at all concerned about the origins of the Western digits. That's not the debate. The debate is about the decimal concept and the concept of having a zero. But I agree that the debate about zero should be reserved for another place.

As for the abacus, you don't sound as if you know the history of the abacus very well. Maybe you need to do some reading. Marcopolo112233 (talk) 06:14, 11 January 2011 (UTC)

Decimal is two independent things: the recursive grouping of units into tens, and the recursive division of units into tenths. They are entirely different things, since one does not imply the other. The exact expression of decimal numbers and decimal divisions varies, but roughly corresponds to the abacus arguments i presented earlier.

One can use repeated denominations, like roman notation (L, X, V, I), and our modern coins. You could use number and weight notation, like 5 lb 3 oz, or 5C2X9, in the manner of chinese and mayans. You could use special symbols for every unit, every ten, every hundred, in the manner of the demotic script. You could use a string of digits, in the manner of the sumerian system. In each case, these would not change the decimal nature, where the units stand in the ratio of 10:1.

The modern notation, of using digits without measure, and significant zeros, exist already in the sumerian number fraction. Only the base has changed, and because ours is a multiple system, rather than a division system, ours has trailing zeros as significant (ie 1 is different to 100, but identical to 001).

The use of recursive fractions, appears in Latin times, derived from the latin weight-fractions (two ounces of an hour), but is represented in the form of nested vulgar fractions (eg 1/15 = 1/20 4/12 in place of 1s 4d in the £). The progression to decimals is then easier to swallow. The reference to an evaluation to 2pi, gives it in base 60, and then 'a system he invented' a decimal representation.

Subtlety carries a fairly hefty sledgehammer. Been there. --Wendy.krieger (talk) 08:44, 11 January 2011 (UTC)

I don't see what your point is. I was just informing you that the average Chinese is not interested in the origins of Western digits, and that your claim about Chinese learning about the abacus from the Romans indicated you didn't seem to know the history of the abacus very well. That's all I said!Marcopolo112233 (talk) 13:48, 12 January 2011 (UTC)

The 2nd last sentence in the 1st paragraph of section "History of the Hindu-Arabic numeral system" is misleading given that the section directly above already puts in serious doubt such claim.

If no-one objects, I will change the wording to remove the ambiguity. The change proposed is as follows:

Original : "On this theory, the ideas were then transmitted..."

Clarified sentence : "According to those who are willing to accept Georges Ifrah's claim despite the seemingly contradictory evidence suggested in the section above, the ideas are believed to have been later transmitted ..."

This change should reduce the disjointed feel of the article. Marcopolo112233 (talk) 05:49, 10 January 2011 (UTC)

Seems to be a BLP violation to me. — Arthur Rubin (talk) 07:24, 10 January 2011 (UTC)

How would this be a BLP violation? Please explain. Marcopolo112233 (talk) 05:48, 11 January 2011 (UTC)

Perhaps not WP:BLP, by WP:SYN. If you remove the clause "despite the seemingly contradictory evidence suggested in the section above", it would be acceptable if sourced and if the source mentions Georges Ifrah. If it named "those who are willing to accept Georges Ifrah's claim", then it would be WP:BLP violation. — Arthur Rubin (talk) 08:24, 11 January 2011 (UTC)

Huh??? I think there is some misunderstanding here.

My understand of the meaning of the phrase "On this theory" is : "According to Georges Ifrah's theory".

So I am not the one who needs to prove what Georges Ifrah said or haven't said. All I am doing is just expanding the existing phrase to make it clear what it is in fact suggesting.

Please let me know if you have a different interpretation of that phrase. Marcopolo112233 (talk) 14:28, 12 January 2011 (UTC)

You're not clarifying, you're editorializing. It probably should be "In this theory", or "According to this theory", rather than "According to those who are willing to accept Georges Ifrah's claim" (see WP:WTA), or the present "On this theory". "Despite the seemingly contradictory evidence" is editorializing and original research. — Arthur Rubin (talk) 16:08, 12 January 2011 (UTC)

The contradiction between the 2 sections are plain obvious. So the "despite ..." part doesn't actually add new information, and therefore is not original research. But to end this debate, I've made the change according to the way you wanted. — Preceding unsigned comment added by Marcopolo112233 (talk • contribs) 10:37, 13 January 2011 (UTC)

On the contrary, the "despite" adds the connotation that Ifrah is wrong. He may be, but the contrary "information" also appears to be due to one scholar, and we are not in a position to judge which is correct. — Arthur Rubin (talk) 19:10, 13 January 2011 (UTC)

There have been some recent changes, back and forth, regarding the wording of the section on Notation. The question seems to be whether the choice of comma or period is dependent upon language or geography/politics. Before we continue to change the article, we should discuss this point and come as close to a consensus as possible. Additionally, any changes should be supported by a reference. My understanding was that the use of a comma does not depend upon language, but rather geography. I thought that the UK used a comma when doing their “maths”. The US definitely uses a period. Clifsportland (talk) 20:48, 10 January 2011 (UTC)

What's the difference between "location" and "geography"? — Arthur Rubin (talk) 08:07, 11 January 2011 (UTC)

typo, fixed. Clifsportland (talk) 21:13, 14 January 2011 (UTC)

I am fairly sure the UK uses the period.

Just an anecdote that might possibly have some tiny relevance: When I was in grad school, I supported myself at times by working on a commercial piece of Windows statistics software. For much of the time I was the sole programmer, working directly with the statistical designer. At some point one of us (or, conceivably, someone in the software publishing house, not sure) got the idea that it might be nice to have the program respect the locale set in the Control Panel as regards commas-v-periods.

So I implemented that and we sent it out for beta. The reaction from a German customer was not nearly as grateful as I expected. He took the position that "English" software (meaning an English-language UI, I guess) ought to use periods; he wanted commas only in "German" software. I thought that was a little strange. But whatever; I added a user preference whereby you could either respect the locale or not ("not" defaulting back to periods). --Trovatore (talk) 22:49, 15 January 2011 (UTC)

The reference to the floor function after mentioning the integral portion of a decimal fraction may be very misleading. For instance truncate(-1.3)=-1, which is NOT equal to floor(-1.3)=-2. This is a common error. Even if that was not the intention of the article, it may still obscure rather than elucidate. — Preceding unsigned comment added by Nielsed (talk • contribs) 17:48, 12 March 2011 (UTC)

Changed to truncation, even though that's proposed to be merged into the floor function article. Thanks. — Arthur Rubin (talk) 19:24, 12 March 2011 (UTC)

Regarding this section, the sentence directly before the common fraction list reads "The decimal fractions are those with a denominator whose only prime factors are 2 and/or 5" (bold added). That is followed by a list of common fractions whose denominator is prime factored by only 2 & 5, until the list item that reads "1/3 =", which fails that particular pattern, as does what follows it. Is this (see Table 4-1) what is meant? Is the list meant to be misleading? Gzuufy (talk) 19:19, 8 May 2011 (UTC)

I believe what that section is meant to indicate is that fractions that are not decimal fractions have infinitely repeating, non-fractional expressions as real numbers. In other words, 1/8, when not written as a fraction, terminates while 1/3 does not. Cliff (talk) 02:41, 9 May 2011 (UTC)

Perhaps the sentence that says, "Any rational number which cannot be expressed as a finite decimal fraction has a unique infinite decimal expansion ending with recurring decimals", which is currently set off from the list with a paragraph break, could be moved to the point in the list right before "1/3=". As it is right now, the list seems mix two different fractional types under what seems a single heading indicating only one type. Gzuufy (talk) 14:59, 9 May 2011 (UTC)

I don't think anybody will disapprove of any improvements you make to the clarity of that section. Edit boldly. Cliff (talk) 20:43, 9 May 2011 (UTC)

Recently there are multiple attempts at disruption without going thru discussion. Sucth disruption is contrary to wiki's policy, should be banned --Gisling (talk) 00:18, 23 June 2011 (UTC).

The 1st sentence of the 1st paragraph of section "Possible Chinese origin of Hindu–Arabic numeral system" starts with the statement "It has been suggested that ...".

The rule of Wikipaedia is that if you cannot provide a source for a claim, you should not state the claim. Given that is the case, either the entire 1st sentence should be removed or if it is accepted, then the qualifier statement "It has been suggested" should not be necessary.

If no-one objects, I will remove that qualifier statement from the sentence. Marcopolo112233 (talk) 06:10, 10 January 2011 (UTC)

I believe we had a source for "it has been suggested", but not for the claim being plausible. — Arthur Rubin (talk) 07:26, 10 January 2011 (UTC)

No, that's not true. I've just checked the entire chapter surronding the page quoted in the source. Nowhere does it say "it has been suggested". So unless you can provide evidence to prove otherwise, I will be changing it tomorrow. (But I don't see what the fuss is. This is a minor change) Marcopolo112233 (talk) 05:48, 11 January 2011 (UTC)

I thought it was a question of the source being reliable. My recollection was that it wasn't reliable, but it was notable, so the correct phrasing is (that source) suggests that.... — Arthur Rubin (talk) 08:09, 11 January 2011 (UTC)

"I thought it was a question of the source being reliable" is false and without any merit. The author Lam Lay Yong was an associate editor of Historia Mathematica and a member of Académie Internationale d'Histoire des Sciences. She also won the higest award in History of Mathematics, how dare you said "unreliable"---00:36, 23 June 2011 (UTC)

What exactly do you mean by "wasn't reliable"? The author was doing a side-by-side comparison of 2 methods. The 2 that are being discussed in this very Wikipaedia article. You can either agree with it or disagree with it. That is, it can only be correct or incorrect. What exactly is unreliable? Marcopolo112233 (talk) 14:08, 12 January 2011 (UTC)

Change "It has been suggested" to "According to Lam Lay Yong", rather than removing it. See the {{refimprove}} tag I just added for reasons. — Arthur Rubin (talk) 16:17, 12 January 2011 (UTC)

I followed the link you provided, but I don't see which part represents your reason.

In any case, as I said, the author did a side-by-side comparison of 2 established methods. Both methods AND the comparison are there for the world to see! ANYONE could have done that comparison. Why would we need to say "according to" him/her? (The reference already gives the information about the author). Do we say "according to" so and so for everything on Wikipaedia? Marcopolo112233 (talk) 11:07, 13 January 2011 (UTC)

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Ok, so I will remove "It has been suggested" if no further objections. If anyone objects, PLEASE give reasons. Marcopolo112233 (talk) 05:40, 16 January 2011 (UTC)

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Done. Marcopolo112233 (talk) 13:22, 17 January 2011 (UTC)

I am the opion that positional decimal system IS a subset of decimal system, it is also the dorminat decimal system in the world to day. It is far more imporatant than general decimal, hence need to be address separately. It is strange that en.wiki does not have article on this imporant topic.---Gisling (talk) 09:13, 23 June 2011 (UTC).

The comment(s) below were originally left at Talk:Decimal/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

History could be in prose. Salix alba (talk) 19:14, 29 September 2006 (UTC) Needs longer lead and more references. Geometry guy 20:51, 9 June 2007 (UTC)

Last edited at 20:51, 9 June 2007 (UTC). Substituted at 20:22, 2 May 2016 (UTC)