Mathematical induction

Form of mathematical proof

Mathematical induction is a method for proving that a statement P ( n) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that is, that the infinitely many cases P ( 0) , P ( 1) , P ( 2) , P ( 3) , … {\displaystyle P(0),P(1),P(2),P(3),\dots }   all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

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