2n - 1 = 4m + 1
Given an m we should be able to find an n, and we can:
n = 2m + 1
(Since m is an integer, so is 2m. Since 2m is an integer so is 2m + 1. Thus n is also an integer.)
So every element of the set is an element of .
In the event you need this to be a proper inclusion, note that not every element of is in because:
4m + 1 = 2n - 1
m = (1/2)(n - 1)
Which means there are values of n such that m is not an integer. So we have:
but not the other way around. Hence this is a proper inclusion.