Example · High school
Terms
| Term | This example | Why |
|---|
| countably infinite |
✓ |
The integers are countably infinite, because they can be listed as $0, 1, -1, 2, -2, \dots$
|
| infinite |
✓ |
|
| countable |
✓ |
$\mathbb{Z}$ is countable because the list $0, 1, -1, 2, -2, \dots$ reaches every integer.
|
| dense set |
✗ |
The integers are not dense in $\reals$, because there is no integer between $1$ and $2$.
|
| finite |
✗ |
$\mathbb{Z}$ is not finite, because the list does not end.
|
| uncountable |
✗ |
|
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