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Mathematics · L5 · Proof Techniques at Scale

A flowchart of the four principal proof strategies used in graduate mathematics.

Mathematics
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Choose a proof strategyNature of claimMathematical inductionProof by contradictionP → Q via ¬Q → ¬PConstructive proofBase caseInductive step: assume P(k), prove P(k+1)Derive logical contradictionNegate the conclusion, derive negated hypothesisExplicit construction or algorithmuniversal statementassume conclusion falseprove contrapositiveexhibit an object

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