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9h
revised Is there enough information to answer this question?
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awarded  Nice Answer
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revised Is there enough information to answer this question?
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answered Is there enough information to answer this question?
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reviewed Close Why does $e^{-x}$ approach $0$ as $x$ gets large?
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reviewed Close General mathematical induction statement for establishing any result.
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revised We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
[In headline terms, given space constraints] I wonder what "We construct the natural numbers to be well ordered" means. If it means we just assume that LNP is true, then fine but the OP might well raise the same worry about that. If the claim is that we construct a sequence of sets in ZFC and prove stuff about that, then the problem shifts to the warrant for the transport principle that takes you from a claim about sets to a claim about numbers (since numbers aren't sets but only putatively modelled by sets). And on that see the last para of my answer ...
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revised We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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revised We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
This is a fancied up version of the observation that induction over the numbers is equivalent to the least number principle. And yes, someone could indeed be helped to see that induction over numbers is in good order by being shown the proof from LNP. But if they then ask what proves the LNP ...
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revised We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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revised We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
Mathematical induction may be given the honorific title of an axiom. But it might still be asked by the OP why we should suppose it is a good axiom to use in reasoning about the numbers we know and love (rather than for reasoning about schnumbers or other beasts).
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answered We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
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revised Where's the foolish part ? Prove that 0/0 = 2
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revised Works of Kurt Gödel
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revised Works of Kurt Gödel
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answered Works of Kurt Gödel
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revised As of August 2015, is the “set” of all gold medalists in the 2016 Olympics a set?
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