Example:Cardinality of the integers

From CS2800 wiki

You might think that adding an infinite number of numbers to the set of natural numbers might make it bigger. But in fact, this is not (necessarily) so. The integers have the same cardinality as the natural numbers:

[math]│\href{/cs2800/wiki/index.php/%E2%84%A4}{ℤ}│ \href{/cs2800/wiki/index.php/Equality_(cardinality)}{=} │\href{/cs2800/wiki/index.php/%E2%84%95}{ℕ}│ [/math]
Proof: cardinality of the integers
The following image clearly defines a bijection:


Details are left as an exercise.