# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

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Concept guide



## [A complete contraction certificate on a finite metric](/en/derivations/derivation-mko-contraction-mapping-theorem-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-contraction-mapping-theorem)

Audit completeness, a unique fixed point and the error bound for a constant self-map on a three-point discrete metric.

Contraction mapping theorem

derivation-mko-contraction-mapping-theorem-01





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