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Proof for cardinality of natural numbers is equal to the cardinality of whole numbers

Hashmi Sahib
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jan 12 '22 at 10:09
  • What are "whole" numbers? Integers? – Mauro ALLEGRANZA Jan 12 '22 at 10:19
  • Hint :

    $f: \mathbb{N}\to \Bbb{Z}$ defined by $$f(n)=\begin{cases} \frac{n}{2} &\text{ } n :even \\frac{-(n+1) }{2}&\text{ otherwise }\end{cases}$$

     – Sourav Ghosh Jan 12 '22 at 10:38
  • You should explicitly define each set because "whole number" is primarily used colloquially (hence not always has a fixed meaning) and in lower school levels (and likely with various meanings around the world), whereas "natural number" is well-known to have two commonly used meanings (see 2nd paragraph here). – Dave L. Renfro Jan 12 '22 at 11:25

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