Jul 5, 2024 · The set of Eudoxus real numbers, denoted ℝ \mathbb{R} , is defined as the initial object in the category of Eudoxus algebras.
Dec 15, 2021 · In this paper by RD Arthan, he calls \mathbb E the Eudoxus reals, and justifies the terminology in the following way.
Oct 1, 2023 · We examine a unique construction of the real numbers which proceeds directly from the integers using approximately linear-endomorphisms with finite error.
May 24, 2004 · This note describes a representation of the real numbers due to Schanuel. The representation lets us construct the real numbers from first principles.
Sep 13, 2018 · Rational numbers can be characterized as Eudoxus real numbers that have a representing functions f:Z→Z whose restrictions f|G to some non- ...
Construction from integers (Eudoxus reals). edit. A ... Eudoxus reals, naming them after ancient Greek astronomer and mathematician Eudoxus of Cnidus.
The Eudoxus real number is a construction of reals directly from integers. Every number is a set of functions ℤ → ℤ growing "almost linearly" (called almost ...
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Aug 6, 2024 · A purely algebraic proof of the fundamental theorem of algebra (without invoking any analytical or topological properties of the real line) is possible.
Oct 29, 2023 · In this project, we present a peculiar construction of the real numbers, called "Eudoxus reals", using Isabelle/HOL.
Sep 22, 2023 · A very cool construction of the non-negative real numbers as sequences of natural numbers satisfying a property he calls “near multiplicativity”.