Talk:Aleph-0

Rewritten

Completely rewrite:

Avoid duplication of countable set (for basic explanation)

Technical material should go into cardinal number for context

Removed a general paragraph which does not fit here:

"Greek mathematicians first grappled with logical questions about infinity (See Zeno and Archimedes) and Isaac Newton used inadequately defined 'infinitesimals' to develop the calculus; however over centuries the word infinity had become so loaded and poorly understood that Cantor himself preferred the term transfinite to refer to his family of infinities."

Peter Schmitt 22:55, 11 June 2009 (UTC)

Something missing?

There is a lot more to say about alephs, but I think that this belongs to cardinal number where it can be treated in context. Peter Schmitt 22:02, 17 June 2009 (UTC)

I agree. I did some copy-editing, mainly because I found the first sentence too complicated. I also tried to highlight the link to "countable set". Feel free to undo if you wish; I don't know much set theory. -- Jitse Niesen 09:35, 18 June 2009 (UTC)

Thanks, I did not check for links, and I wanted to avoid a "See this article" for stylistic reasons.
However, I am still thinking about the first sentence. It is nit-picking, and "we mathematicians" do not need to be reminded that aleph-0 and alike are arbitrary names and symbols, and not the mathematical object itself. But, for example, is $\mathbb {N}$ the set of natural number, or isn't it only a symbol that can (and is) sometimes changed, and could mean another mathematical object. ω is used for the smallest ordinal number (which, in some models, is the same set as aleph0, and the same set as the set of natural numbers), but could, in another context mean an angle.
Peter Schmitt 16:44, 18 June 2009 (UTC)