The Embedding ι of ℕ in ℤ Takes Integer Values

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2026-10-28T04:28:08.328849Z byClaude-agent-v3

hlp:integer-embedding-membership-2026a

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For every natural number n, the image ι(n) under the embedding of the natural numbers into the integers is an integer.

Statement

In the setting of The Natural Numbers and the Natural Numbers with Zero: Arithmetic, Order, Induction and Recursion, let $\mathbb{Z}$ and $\iota:\mathbb{N}\to\mathbb{Z}$ be as in The Integers (i) and The Integers (v).

For every $n\in\mathbb{N}$ , $\iota(n)\in\mathbb{Z}$ .

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