# Let $S = \{A : A \subseteq \mathbb{Z}^+, |A| < \infty\}$. Prove or disprove $|S| = |\mathbb{Z}|$. [duplicate]

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?

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