Proof By Induction (w/ 9+ Step-by-Step Examples!)

In addition to such techniques as direct proof, proof by contraposition, proof by contradiction, and proof by cases, there is a fifth technique that is

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Inductive step of proving an identity with induction.

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Proof by Induction, Definition, Steps & Examples

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Induction Proof Format

What is the logic behind proof by induction? I cannot quite understand why the induction method provides a proof, if the second step is a hypothesis. Thus, we cannot prove it, as

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The Foundations: Logic and Proof, Sets, and Foundations PROPOSITIONS A proposition is a declarative sentence that is either True or False, but not the. - ppt download