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countable

A set $S$ is countable if there exists a bijection between $S$ and some subset of $\mathbb{N}$ .

All finite sets are countable.

countable is owned by Kevin Ferguson.

How to Cite This Entry

Kevin Ferguson. "countable" (version 2). PlanetMath.org. Freely available at http://planetmath.org/Countable.html.

Classification

AMS MSC:

03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)

Pending Errata and Addenda

None.

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Discussion

flesh out a little? by odenskrigare on 2008-06-05 01:07:19

I guess there's not much else to say here, but I'd like to add that an infinite set in which a finite interval contains a finite number of elements is countable, where an infinite set in which a finite interval contains an infinite amount of elements is uncountable, then give integers vs. reals as an example. I find that definition really useful.

[ reply | up ]

Re: flesh out a little? by Pedro A. Fernandez on 2008-06-05 02:10:03
- Re: flesh out a little? by odenskrigare on 2008-06-05 05:30:04
- - Re: flesh out a little? by J. Pahikkala on 2008-06-05 06:29:50
  - - Re: flesh out a little? by odenskrigare on 2008-06-05 15:30:07
Re: flesh out a little? by ratboy on 2008-06-05 04:33:47
- Re: flesh out a little? by odenskrigare on 2008-06-05 05:31:00

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