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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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 $\displaystyle m < n$ then $\displaystyle n = m + c, c > 0$. Assume $\displaystyle n < m$. Then $\displaystyle m + c < m \implies c < 0$. But we said $\displaystyle c > 0$. So $\displaystyle n < m$ can not occur.
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