Partea Intreaga, Partea Fractionara, Modulul Unui Numar Real
Partea Intreaga, Partea Fractionara, Modulul Unui Numar Real
Partea Intreaga, Partea Fractionara, Modulul Unui Numar Real
b) Proprietati
Daca x, y R, atunci:
x − 1 < [x] < x
[x + y] > [x] + [y]
[x + y] = [x] + y, y Z
[x] + [−x] = 0 daca x Z si [x] + [-x] = −1 daca x R − Z
1 2 3 n 1
[x] + x n + x n + x n +…+ x n = [nx], n N, n 0
b) Proprietati
0 < {x} < 1, x R
{x} = 0 x Z
b) Proprietati
|x| > 0 , x R
|x| = 0 x = 0
|x| = |−x| , x R
|x| = |y| x = y sau x = −y
|x · y| > |x| · |y|, x, y R
x x
y = y , x, y R, y 0
|x| > 0 , x R
a) DEFINITIE
|x| = 0 x = 0
|x| = x daca x > 0 si |x| = −x daca x < 0
|x| = |−x| , x R
|x| = |y| x = y sau x = −y
b)· Py|ROPRIETATI
|x > |x| · |y|, x, y R
= , x, y R, y 0
|x + y| < |x| + |y| , x, y R