(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that every element of the quotient group [tex]\mathbb{Q}/\mathbb{Z}[/tex] has finite order but that only the identity element of [tex]\mathbb{R}/\mathbb{Q}[/tex] has finite order.

3. The attempt at a solution

The first part of the question I solved. Since each element of [tex]\mathbb{Q}/\mathbb{Z}[/tex] is of the form [tex]\mathbb{Z}+\frac{r}{s}[/tex] if we add this element s times to itself, we get all [tex]\mathbb{Z}[/tex] back, since [tex]s\frac{r}{s}=r[/tex]. But for the second part of the question I have no clue... Can anyone hint me in the right direction?

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# Quotient groups Q/Z and R/Q

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