Give an example of two infinite subsets A and B of the real numbers such that A $\ne$ B (A not equivalent B). Justify why they are not equivalent.
Here's what I did:
Since $\mathbb{Z}$ is a subset of the real numbers, let A = { $2x$ : $x$ $\in$ $\mathbb{Z}$ } and B = { $2x + 1$ : $x$ $\in$ $\mathbb{Z}$ }
A $\ne$ B because $2x + 1$ $\ne$ $2x$ .
Is this an acceptable answer or is there a better example to use?