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Prove that $\mathbb{Z}_m$ and $\mathbb{Z}_n$ have the same cardinality iff m=n
In the following proof, $\mathbb{Z}_n= \{ 1,2,....n \} $
After $g$ is defined , they defined the composition $gof$ and then they defined $h$ by removing the last ordered pair $(n+1,m)$ from the ...
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Defining Addition of Natural Numbers as the Algebra of 'Push-Along' Functions
Let $N$ be a set containing an element $1$ and $\sigma: N \to N$ an injective function satisfying the following two properties:
$\tag 1 1 \notin \sigma(N)$
$\tag 2 (\forall M \subset N) \;\text{If } ...
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