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# mathematical induction

mathematical induction

- A method of proof in which a statement is proved for one step in a process, and it is shown that if the statement holds for that step, it holds for the next.

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## Word History and Origins

Origin of mathematical induction^{1}

First recorded in 1830–40

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## Example Sentences

We can ascend only by mathematical induction, which alone can teach us something new.

From Project Gutenberg

This mode of reasoning is none the less a true mathematical induction which differs from ordinary induction only by its certitude.

From Project Gutenberg

To all such numbers, proofs by mathematical induction can be validly applied.

From Project Gutenberg

It may be noticed that (iv) is the familar principle of mathematical induction.

From Project Gutenberg

This is the principle of what is called “mathematical induction.”

From Project Gutenberg

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