Weak induction proves a statement for natural numbers by assuming it's true for the immediately preceding case. This contrasts with…
Strong induction strengthens the inductive hypothesis, allowing the assumption that the proposition holds for all smaller cases. This powerful technique…
A method of mathematical proof where a statement is divided into several exhaustive cases. The statement is then proven to…
The inductive step of a proof by induction demonstrates that if a property holds for any arbitrary element 'n', it…
A formal logic and mathematics proof technique. It verifies properties for basic formulas and ensures they are maintained through operations…
An indirect proof, also known as proof by contradiction, involves assuming the opposite of what you want to prove. If…
Contraposition is a logical principle establishing the equivalence between a conditional statement and its contrapositive. It transforms 'If P, then…
The basis step, or base case, is the foundational element of a proof by mathematical induction. It establishes the truth…