1
vote
2answers
64 views

equivalence classes and cardinality

I need to prove that every equivalence class created by the equivalnce relation $\sim$ on $\mathbb{R}$, that is defined by: $a\sim b \Leftrightarrow (a-b) \in \mathbb{Q}$, is $\aleph_0$. Furthermore, ...
-3
votes
1answer
85 views

Rational numbers and cardinality of some subset set of them.

Let $G$ be the set of rational numbers of the form $m/n$ , where $m,n$ are positive integers and $n \leq g $ for some possitive integer $g$. Suppose it is bounded by $1/k$ , k is a positive integer ...
17
votes
4answers
431 views

What do the cosets of $\mathbb{R} / \mathbb{Q}$ look like?

$\newcommand{\R}{\Bbb R}\newcommand{\Q}{\Bbb Q}$ Looking at the group of real numbers under addition $(\R, +)$ it contains the (normal) subgroup of rational numbers $(\Q, +)$. I am wondering how to ...