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Thread: 3 solved proofs for those who need help

  1. #1
    Senior Member x3bnm's Avatar
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    3 solved proofs for those who need help

    1) There exists an integer n such that for every integer m, we have m ≤ n
    2) If n^2 is even, then n is even
    3) Pigeonhole Principle

    Reference: Different Websites

    3 proofs.pdf
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  2. #2
    MHF Contributor

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    Re: 3 solved proofs for those who need help

    The first of those, that "there exist an integer n such that for every m we have m<n" is simply NOT TRUE! For any integer, n, m= n+ 1 does not satisfy "m< n". So of course your "proof" is incorrect. The error is where you say "There exists an integer m such that m > n. Since for any m, we have that m > n is true". You have jumped from
    "there exists and integer m" to "for any m" and the second does NOT follow from the first.
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