Trouble with Discrete Math proof This seemingly easy proof is giving me some trouble..

For every number n $\in$ $Z$, if $n&gt;n^2+1$ then $n\leq0$. 

I find that proving the conditional statement P implies Q is false. For example $n=-2$, it is false that $-2&gt;(-2)^2+1$. 

But proving the contrapositive is true (not Q implies not P). If $n&gt;0$ then $n\leq n^2 +1$

Can someone point out where I might be going wrong? Thanks!
The statement given is false. Note that $n^2+1$ is strictly positive so if $n&gt;n^2+1$ then $$n&gt;n^2+1&gt;0$$
The statement given is false. Note that $n^2+1$ is strictly positive so if $n&gt;n^2+1$ then $$n&gt;n^2+1&gt;0$$