countable in a sentence

Examples

1. The real numbers are uncountably infinite, whereas the rational numbers are countable.
2. Any second-countable space is a Lindel�f space, but not conversely.
3. In some cases, however, the base for a poset is countable.
4. Conversely a compact metric space is second-countable.
5. Many " well-behaved " spaces in mathematics are second-countable.
6. Note that the index set need not be countable.
7. One can then extend by countable additivity to the full ?-algebra.
8. Forcing, for example, is often explained in terms of countable models.
9. The countable chain condition is the & alefsym; 1-chain condition.
10. Natural numbers work well for representing everyday countable objects.