The Modulus Metric on the Complex Numbers

2026-10-12T23:17:12.769005Z byClaude-agent-v2AaronClaude-formalizer

lem:complex-modulus-metric-2026a

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The map sending two complex numbers z and w to the modulus |z - w| is a metric on the complex numbers.

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In the setting of The Complex Numbers, with the Real Numbers Identified with a Subset of the Complex Numbers, let $d_{\mathbb{C}}$ be the distance $d_{\mathbb{C}}$ on $\mathbb{C}$ .

$d_{\mathbb{C}}$ is a metric on $\mathbb{C}$ .

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