Mathematical induction
= Mathematical induction
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= Induction
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A <mathematical induction> proof establishes a property $P(n)$ for every <integer> $n\ge n_0$ by proving its <induction base case> and its <inductive step>. If a counterexample existed, the <well-ordering principle> would give a least one; its predecessor and the inductive implication exclude it. The starting case excludes a counterexample at $n_0$.