This seemingly easy proof is giving me some trouble..
For every number n $\in$ $Z$, if $n>n^2+1$ then $n\leq0$.
I find that proving the conditional statement P implies Q is false. For example $n=-2$, it is false that $-2>(-2)^2+1$.
But proving the contrapositive is true (not Q implies not P). If $n>0$ then $n\leq n^2 +1$
Can someone point out where I might be going wrong? Thanks!