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This is a question from someone who is very new to math, so please excuse my ignorance.

In a couple of places, I have learned proof by induction, which claims to prove for a set of all integers.

A thought occurred to me (perhaps a silly thought): What proof is there that massively high/low numbers do not have some special properties that might invalidate some proofs? Is there rigorous logical proof that this is not true?

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Really high/low numbers do not have special properties because of definition. Part of the very definition of natural numbers is that they follow induction. So if something doesn't follow induction, then it isn't a number.

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  • $\begingroup$ Can you tell me where to find this definition of natural numbers? I think this was the missing piece for me. $\endgroup$ – baordog Mar 22 '15 at 17:34
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    $\begingroup$ @baordog: Look for "Peano axioms". $\endgroup$ – PhoemueX Mar 22 '15 at 17:35

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