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Math Help - [SOLVED] Proof involving natural numbers

  1. #1
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    [SOLVED] Proof involving natural numbers

    Suppose m,n e N. Show that m < n and n < m cannot both occur.

    This is obvious, but I having trouble proving it mathematically.

    Any advice? Thanks in advance.
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Suppose m,n e N. Show that m < n and n < m cannot both occur.

    This is obvious, but I having trouble proving it mathematically.

    Any advice? Thanks in advance.
    If m < n then n = m + c, c > 0.


    Assume n < m.

    Then m + c < m \implies c < 0.

    But we said c > 0.

    So n < m can not occur.
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