Question

Which sets of numbers are closed under division?

Answer 1

nonzero rational numbers
because it is impossible to divide our way out of the set of
nonzero rational numbers. For example we can start with two nonzero
rational numbers, say 73/99 and 21/13, which are indeed nonzero rational number. So we cannot
divide our way out of the set of nonzero rational numbers. Since this
is not possible, the set of nonzero rational numbers is indeed closed
under division.