Comments on: Example of an Infinite Group Whose Elements Have Finite Orders https://yutsumura.com/example-of-an-infinite-group-whose-elements-have-finite-orders/ Fri, 15 Dec 2017 07:04:16 +0000 hourly 1 https://wordpress.org/?v=5.3.4 By: Yu https://yutsumura.com/example-of-an-infinite-group-whose-elements-have-finite-orders/#comment-4551 Fri, 15 Dec 2017 07:04:16 +0000 https://yutsumura.com/?p=5187#comment-4551 Note that each element in the group $\Q/\Z$ is of the form $q+\Z$, where $q\in $\Q$. We say that $q$ is a representative for the element $q+\Z$.

For the second part, $m$ is not necessarily $0$. But $m+\Z$ is equal to $0+\Z$.

]]> By: Lalitha https://yutsumura.com/example-of-an-infinite-group-whose-elements-have-finite-orders/#comment-4549 Fri, 15 Dec 2017 06:40:39 +0000 https://yutsumura.com/?p=5187#comment-4549 Please explain what are representatives in Q/Z ? You mean elements of Q/Z?
“This implies that the representatives of Q/Z are rational numbers in the interval [0,1).”

From this sentence please explain the remaining part once again :
“On the other hand, as each element of Q/Z is of the form mn+Z for m,n∈Z, we have…”
Why m=0? and why is the order of any element in Q/Z is atmost n ?

Thanks

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