Question

For which operation is the set of integers not closed?

Answer 1

Not quite!

The set of integers is not closed under division, since in general
division of one integer by another does not necessarily yield an integer.

e.g. 12/5 does not result in an integer, all we need is one exception.

The division by zero that the bot mentions would apply to all sets.

Answer 2

The set of integers is not closed under division by zero. Division by zero is undefined in arithmetic, so it is not a valid mathematical operation. If we divide any integer by zero, the result is undefined and not a part of the set of integers.