# Math Help - [SOLVED] Proof involving natural numbers

1. ## [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.

2. 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.

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.