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Mathematics-Online lexicon:

Mathematical Induction


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Statements with natural numbers as their parameters can be proved by the Principle of Mathematical Induction. If $ A(n)$ is a statement that depends on $ n\in\mathbb{N}$, the method of proof consists of the following two steps:

This establishes the truth of $ A(n)$ for all $ n\in\mathbb{N}$ .

The Principle of Mathematical Induction successively infers the truth of a statement $ A(n+1)$ from the previous statement $ A(n)$. Therefore, if in the base step $ A(n_0)$ is verfied for some $ n_0>1$ rather than $ A(1)$, then the statement has only been proved for $ n \geq n_0$.

(Authors: Kimmerle/Abele)

see also:


[Examples]

  automatically generated 6/11/2007