The question says \"Find all generators of an infinite cyclic group G =<a>.\" ..

Question

The question says "Find all generators of an infinite cyclic group G =<a>." .... I have no idea. I don't really understand what it is eventalking about. Can you please help me? I need alot of explanationwith how you got the answers. Thanks so much!!! The question says "Find all generators of an infinite cyclic group G =<a>." .... I have no idea. I don't really understand what it is eventalking about. Can you please help me? I need alot of explanationwith how you got the answers. Thanks so much!!!

Explanation / Answer

a generator of a cyclic group is simply an element of the group which has the characteristic that when you repeatedly perform the group operation you end up with the whole group, i.e., generate the whole group. For example the natural numbers  can be written with the addition operation. This means that adding 1 over and over gets you the entire group. So your generator is a.

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