The empty set $\emptyset$
Definition: empty set
Terms
| Term | This example | Why |
|---|---|---|
| open set | ✓ | The empty set is open in $\reals$, because it has no points, so the condition on its points holds vacuously. |
| closed set | ✓ | The empty set is closed in $\reals$, because its complement, $\reals$, is open. |
| finite | ✓ | The empty set is finite, because it has $0$ elements, and $0$ is a finite number. |
| countable | ✓ | The empty set is countable, because it is finite. |
| empty set | ✓ | |
| countably infinite | ✗ | |
| uncountable | ✗ | The empty set is not uncountable, because it is finite. |