Real numbers modulo $1$.

Question

In teaching material of my professor I read "where $x_1,x_2,...,x_m$ are distinct real numbers modulo $1$". What is the definition of numbers modulo $1$? Intuitively I would say that there exist a number c such that $$x_n=c\ n \ \ \forall n \in\mathbb N$$ is it right?

This is the circle group $, \Bbb R/\Bbb Z,,$ e.g. see this question. and here too. — Bill Dubuque, May 03 '15 at 16:11

score 5 · Accepted Answer · answered May 03 '15 at 09:03

5

Not quite. Usually $x$ and $y$ are said to be distinct real numbers modulo $1$ if $x-y$ is not an integer. The intuition being that numbers are congruent modulo $n$ if their difference is an integer multiple of $n$.

answered May 03 '15 at 09:03

jgon

28,469

thank you; $x-y$ should not be integer, or it should not be integer less than $1$? – Lely May 03 '15 at 09:18
1

@Lely Just should not be an integer. The relation is symmetric. – jgon May 03 '15 at 09:18

Real numbers modulo $1$.

1 Answers1