- #1
Mr Davis 97
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Homework Statement
Prove that if ##a > 1##, then the sequence ##a^n## is unbounded.
Homework Equations
The Attempt at a Solution
We need to show that ##\forall M \in \mathbb{R}~\exists N \in \mathbb{N},~~ a^n > M##. To do this I thought maybe we could let ##N = \operatorname{ceil}(\log_a(M))+1##, so that we are guaranteed that ##a^N > M##, but I don't think this will work for several reasons. One, ##M## could be negative. And two, I formally haven't defined the notion of logarithm yet. What approach should I take then?