Question

Mathematical Induction question

Answer 1

Suppose I want to prove that
\[a^ma^n=a^{m+n}\]I believe my base case would be to fix m and show \[a^ma^1=a^{m+1}\]
But I'm not sure if I should be showing \[a^1a^1=a^{1+1}\]

TL;DR: What should my base case be (and do I have multiple base cases)?

Answer 2

*Also, it's for m,n>0

Answer 3

somewhat tricky because you have both \(m\) and \(n\)
best idea i think is to fix \(n\) and then use induction on \(m\)
don't try to do it both at once, it will not work

Answer 4

Kk, thanks!