# [SOLVED] Proof involving natural numbers

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• Feb 12th 2009, 10:14 PM
jzellt
[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.
• Feb 12th 2009, 10:20 PM
Prove It
Quote:

Originally Posted by jzellt
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.