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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
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| ``Re: Proof of Chebyshev's inequality by induction''
by ratboy on 2007-03-03 21:38:55 |
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| > Beg to disagree: there's only one way to prove that a
> certain set S of natural numbers is equal to the set N of
> all natural numbers, and that is to show that S is
> inductive: (i) 1 belongs to S; (ii) for any n, 'n belongs to
> S' implies 'n+1 belongs to S'.
Many properties of natural numbers can be proved to hold for all natural numbers in weak theories of arithmetic, such as Robinson's Q, that do not include induction among their axioms. Also, zero is usually considered to be a natural number. |
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