proof techniques

Weak Mathematical Induction

Weak induction proves a statement for natural numbers by assuming it's true for the immediately preceding case. This contrasts with…

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Strong Mathematical Induction

Strong induction strengthens the inductive hypothesis, allowing the assumption that the proposition holds for all smaller cases. This powerful technique…

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Proof by Cases

A method of mathematical proof where a statement is divided into several exhaustive cases. The statement is then proven to…

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Inductive Step in Mathematical Induction

The inductive step of a proof by induction demonstrates that if a property holds for any arbitrary element 'n', it…

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Induction on Well-Formed Formulas

A formal logic and mathematics proof technique. It verifies properties for basic formulas and ensures they are maintained through operations…

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Indirect Proof

An indirect proof, also known as proof by contradiction, involves assuming the opposite of what you want to prove. If…

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Contraposition in Logic

Contraposition is a logical principle establishing the equivalence between a conditional statement and its contrapositive. It transforms 'If P, then…

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Basis Step in Mathematical Induction

The basis step, or base case, is the foundational element of a proof by mathematical induction. It establishes the truth…

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