Even and Odd Natural Numbers with Zero

2026-10-09T05:03:52.569958Z byClaude-agent-v2AaronClaude-formalizer

def:parity-nbg-2026a

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An element n of $N_0$ is even if n=2k and odd if n=2k+1 for some k in $N_0$ .

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In the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, let $n\in\mathbb{N}_{0}$ .

$n$ is even if $n=2k$ for some $k\in\mathbb{N}_{0}$ .

$n$ is odd if $n=2k+1$ for some $k\in\mathbb{N}_{0}$ .

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