Example · High school
Terms
| Term | This example | Why |
|---|
| infinite |
✓ |
$n \mapsto 2n$ is a bijection from $\nats$ onto the even numbers, a proper subset.
|
| countably infinite |
✓ |
$\nats$ is countably infinite, and so infinite, because it can be listed as $0, 1, 2, \dots$.
|
| countable |
✓ |
$\nats$ is countable because the list $0, 1, 2, \dots$ reaches every natural number.
|
| finite |
✗ |
$\nats$ is not finite, because the list does not end.
|
| bounded |
✗ |
$\nats$ is not bounded, because for every $N > 0$, we can pick $n \in \nats$ such that $n > N$.
|
| compact |
✗ |
$\nats$ is not finite or compact.
|
| uncountable |
✗ |
|
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