Showing that there is no embedding between groups

[gottfried]

Homework Statement

Show that there exists and embedding or show that an embedding can't exist between Z₃ and Z.

The Attempt at a Solution

I've tried to find an embedding and can't so I've decided that an embedding can't exist but how does one show this?

Any suggestions would be great.

 

[micromass]

Hint: in $\mathbb{Z}_3$, we have 1+1+1=0.