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# Element of Finite Order

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Prove that every element of Q/Z has finite order, where Q is the set of rational numbers with group operation + and Z is the set of integers.

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#### Solution Preview

First of all, the group operation here is addition. Q is the set of rational numbers, Z the set of integers. Neither one of these sets is finite. There are an infinite number of integers and an infinite number of rational numbers (these do include the integers).

So it's not going to do any good to suppose for a minute that either of these groups has finite ...

#### Solution Summary

It is proven that every element of Q/Z has finite order, where Q is the set of rational numbers with group operation + and Z is the set of integers.

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