I'm supposed to prove this using induction. Any advice?
let a be a real number. Prove by induction on n that a^(m+n) = (a^m)(a^n) for all positive integers m,n.
Thanks for any advice.
i think it's ridiculous to use induction because
a^(m+n) = aaaaaaaaa...aaaaa m+n times
and a^(m)a^(n) = aaaa...aaa (m times) x aaaa....aaaa (n times)
but if you used induction,
a^(m+1) = aaaaa...aaaaa (m times) x a (1 time)
and then if a^(m + n) = a^(m)a^(n), then
a^(m + (n +1)) = a^((m + n) +1) = a^(m + n)a^(1) = a^(m)a^(n)a^(1) = a^(m)a^(n+1)
sorry if it's confusing