For natural numbers, I would like to prove that if $m < n$, then $k^m < k^n$ for $k$ not $0$ or $1$. Induction seems viable, but I don't know which variable to induct on. Any suggestions?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top