What do finite, infinite, countable, not countable, countably infinite mean? [duplicate] Ask Question Asked 13 years, 5 months ago Modified 13 years, 5 months ago

Dec 12, 2013 · Well, the assertion is that, if you have a countable collection of sets which are countable themselves, then the union of all elements in the collection is also countable.

9 $\mathbb {R}$ with standard topology is second-countable space. For a second-countable space with a (not necessarily countable) base, any open set can be written as a countable …

My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural …

Nov 25, 2015 · If you can achieve a bijection of the members of the sets to $\Bbb N$, the the set will be called countable, and moreover ,if it is infinite, then it is countably infinite. So, the set …

Jan 22, 2025 · The fact that it can be expressed as a countable, disjoint union, of some intervals is known and has been dealt with on SE in multiple posts like in here or here just to name a …

Feb 6, 2015 · From the fact that cartesian product of countably infinite sets is countably infinite, $\mathbb Z \times \mathbb N$ is countable. Because the domain of injection to a countable …

Mar 16, 2015 · The definition for 2nd countable topological space is that "the topological space has a countable basis." My confusion is whether or not they mean countably infinite basis only.

Note that you cannot have two (or more) disjoint co-countable sets.

Fine. $\mathbb Q$ is an infinite set. An infinite set is countable if it has an injection into $\mathbb N$. Or into any countable set, such as $\mathbb Z$, which you already know is countable.