This problem appears as an exercise labeled middle-Level problem in the book of Abstract Algebra by I. N. Herstein (Third edition) section 2.1 Definitions and Examples of Groups, it says:

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> If $G$ is a finite group, prove that, given $a\in G$, there is a positive integer $n$, depending on $a$, such that $a^n = e$
> 
> 
> 

I state the negation as:

If $G$ is a finite group, then there exists $a \in G$ which for all integer $n$, depending on $a$, such that $a^n \neq e$.

Am I correct at this point? Is this the right way to negate the statement? If so the proof is very easy now, but if is not, which is the correct way? Is the same as contrapositive?

Edit
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Now thanks to your replies I think I spot some errors at my orginal negation, now I will write something like:

If $G$ is a finite group, then there exists $a \in G$ which, for all positive integer $n$, $a^n≠e$. Is this now correct?