Talk:Epimorphism from Integers to Cyclic Group

From Wikipedia: :

"The name "cyclic" may be misleading: it is possible to generate infinitely many elements and not form any literal cycles; that is, every $g^n$ is distinct. (It can be said that it has one infinitely long cycle.) A group generated in this way is called an infinite cyclic group, and is isomorphic to the additive group of integers $\Z$.

Furthermore, the circle group (whose elements are uncountable) is not a cyclic group—a cyclic group always has countable elements."

So there is no need to refer to a "countable" cyclic group - all cyclic groups are countable (or finite). --Matt Westwood 06:34, 17 December 2008 (UTC)