the question goes like this :
Write down all the numbers in this set.
A={x€Z | all n€Z+ fall into x/n € Z}
I hope I’m translating it correctly
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If set A is defined as all integers x such that for all positive integers, x/n is an integer, then A is contains only one element, 0.
Why?
0/n = 0 for all n.
For non-zero integers, I can always find an n such that x/n isn't an integer. Let n = |x|+1. For positive x, x/n = x/x+1 = 1/(1+1/x)