If it were $\mathbb{R}$ instead of $\mathbb{Z}$, I could figure it out: just construct $2$ bijections. For example, map $\mathbb{R}$ to $(0,1)$ and then map $(0,1)$ to $\mathbb{R}$ in tangent function. However, when it comes to a set with discrete elements, this method doesn't work. Is there any other ways?

  • $\begingroup$ What do you think? If you think that $|S|=|\mathbb Z|$, then fining a bijection would still be the way to go. $\endgroup$ – Babelfish Mar 12 '19 at 15:42
  • $\begingroup$ These two links have infinitely many more possible duplicate suggestions under "Linked" and "Related" in the part to the right of the question. $\endgroup$ – Asaf Karagila Mar 12 '19 at 15:47