Set of Common Divisors of Integers is not Empty

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Let $a, b \in \Z$ be integers.

Let $S$ be the set of common divisors of $a$ and $b$.

Then $S$ is not empty.


From One is Common Divisor of Integers:

$1$ is a common divisor of $a$ and $b$.

Thus, whatever $a$ and $b$ are:

$1 \in S$

The result follows by definition of empty set.