Showing that there is no embedding between groups

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

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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