$\mathbb{R}$ is closed under division

Question

The set of real numbers $\mathbb{R}$ is closed under division. Does that mean $0$ is also considered?
more specifically, should it be $\mathbb{R}-\{ 0 \}$?
because division by $0$ is not defined.

Answer 1

The real numbers aren't closed under division unless you don't include zero. So it is like you said: $\mathbb{R}-\{0\}$ is closed under division since we don't encounter that problem.