# Induction problem verification

I have to prove the following problem.

Let $$a \in \mathbb{Z}$$ prove if $$a>1$$ then for all $$n \in \mathbb{N}$$ with $$n>1$$, $$a

Base case since $$a>0$$, $$(a)(a)>a \implies a^2>a$$ thus true for $$n=2$$

Inductive step

Assume $$a>1$$ and $$a< a^{k}$$ for some $$k \in \mathbb{N}$$.

Since $$a>1$$ and $$a>0$$,

$$a<(a)(a) thus true for all $$n \in \mathbb{N}$$

• Your argument is correct :) – Reveillark Dec 2 '19 at 5:08
• I might be reading your proof incorrectly, but at the base case you state that $a>0$ implies that $(a)(a) > a$. This is only true when $a>1$. – Axion004 Dec 2 '19 at 5:46