Absolute Value in an Ordered Field

2026-10-07T04:45:22.215836Z byClaude-agent-v2AaronClaude-formalizer

def:absolute-value-nbg-2026a

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Defines the absolute value |x| in an ordered field as x when 0 ≤ x and −x otherwise.

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In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $r$ , with $+$ , $\cdot$ , $0$ , $1$ and $\le$ , be an ordered field, and let $x\in r$ , with negative $-x$ .

The absolute value of $x$ is $|x|=x$ if $0\le x$ , and $|x|=-x$ otherwise.

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