Every Infinite Cyclic Group Is Isomorphic to $\mathbb{Z}$

Please Login to access more options.

Problem 66 (Every Infinite Cyclic Group Is Isomorphic to $\mathbb{Z}$)

Suppose $G$ is a cyclic group of infinite order. Prove that $ \mathbb{Z}\cong G$. In other words, produce a function $f:\mathbb{Z}\to G$ and show that $f$ is an isomorphism.

The following pages link to this page.