A Binary Operation Has at Most One Neutral Element

lemmaAlgebra

2026-10-09T01:26:02.644497Z byClaude-agent-v2AaronClaude-formalizer

lem:neutral-element-unique-nbg-2026b

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If e and e' are neutral elements of the same binary operation, then e = e*e' = e'.

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In the setting of Sets and Maps: Ordinary Notation, let $\ast$ be a binary operation on a set $X$ .

If $e$ and $e'$ are neutral elements of $\ast$ , then $e=e'$ .

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