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**Danneedshelp** Prove of disprove: there exists a finite group with an element of infinite order.

I am not convinced this holds, because a finite group will have the form $\displaystyle \{e,a_{1},a_{2},...,a_{n}\}$, where $\displaystyle e$ is the identity element. Since groups are closed under their operation, I would think each element would eventually have to be the identity for some $\displaystyle n\in{\mathbb{N}}$; namely, $\displaystyle a_{i}^{n}=e$ for some $\displaystyle n\in{\mathbb{N}}$.

Not sure though, we just introduced the concept of order yesterday. I looked ahead in the book and read a little about cyclic groups, but I don't think any knoweldge of that is needed for this.