Talk:Countable set/Draft

Shouldn't this live at enumerability? And an article about countable sets should live at countability, I should think, as well. I don't know, I'm not giving an order, I'm just saying how I would do it. There's an issue to think through here. --Larry Sanger 12:45, 22 February 2007 (CST)

Actually, I think I agree with you. I should have titled this article Countability. Can you remind me how to rename an article? Thanks. --Nick Johnson 13:55, 22 February 2007 (CST)

suggestions

1. I agree that a better article title would be countable (or countability).
2. The current version has the sentence: "Inductive proofs rely upon enumeration of induction variables." Not really: induction is a procedure that applies to the natural numbers and only the natural numbers. It might be that a function proving countability of a set might translate one problem into another problem for which induction is relevant, but that's not the same thing.
3. Narrative! The amazing fact about infinite sets is that there are lots of different sizes of them. An article on countability should introduce the reader to this paradoxical point of view, take them through the idea of using bijections to define "same size" (cardinality), and then discuss the role of countable sets in this hierarchy. Cantor's proof of the uncountability of the reals should of course be mentioned. Remember that the vast majority of readers will not know what a one-to-one function is nor the significance of the word "onto", as opposed to simply "to". If one needs to know the topic already to understand our article, then the article isn't going the right direction.

- Greg Martin 09:41, 20 May 2007 (CDT)

Use of term "enumerable"

The article currently states that "an enumerable set has the same cardinality as the set of natural numbers." That's true about infinite sets, but isn't the word "enumerable" sometimes used about finite sets as well?

Ragnar Schroder 00:33, 29 June 2007 (CDT)