Brian Bi
Exercise 2.3.3(a) Let $$S$$ be a nonempty, possibly infinite set of integers. If $$S = \{0\}$$, then define the GCD to be 0. Otherwise, the subgroup of $$\mathbb{Z}^+$$ generated by $$S$$ contains a least positive element $$d$$ and by Theorem 2.3.3, this subgroup is precisely $$d\mathbb{Z}$$. We define the GCD of $$S$$ to be $$d$$.