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#### MI5

##### New member

- Sep 8, 2013

- 8

This is the proof from my book. If $a \ge 0$, then $a = a-d\cdot 0 \in S$. If $a < 0$, let $x = -y$ where $y$ is a positive integer.

**Since $d$ is positive, we have $a-dx = a+dy \in S$ for sufficiently large $y$.**Thus $S$ is nonempty.

Could someone explain sentence that I've bolded? It's not clear to me.