# 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 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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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 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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