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# Difference between revisions of "Talk:Aleph-0"

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Jitse Niesen (Talk | contribs) (→Something missing?: reply) |
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::: Thanks, I did not check for links, and I wanted to avoid a "See this article" for stylistic reasons. <br> 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''' <math>\mathbb N</math> 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. <br> [[User:Peter Schmitt|Peter Schmitt]] 16:44, 18 June 2009 (UTC) | ::: Thanks, I did not check for links, and I wanted to avoid a "See this article" for stylistic reasons. <br> 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''' <math>\mathbb N</math> 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. <br> [[User:Peter Schmitt|Peter Schmitt]] 16:44, 18 June 2009 (UTC) | ||

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+ | :::: Ah, so that is why you wrote "traditionally". That confused me. I see your point, but the article on [[Paris]] also starts with "Paris is the capital of France", even though one could also see "Paris" as an arbitrary name, which can even refer to other things (Greek hero, various cities in the US). I think it would be over the top to write "Paris is a string of letters which often refers to the current capital of France." But going back to this article, would you prefer it if we wrote "aleph-0 denotes …" instead of "aleph-0 is …"? | ||

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+ | :::: You are right that the "see this article" looks weird, so I removed it again. Let's hope that the bold font is enough to attract attention to the link. | ||

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+ | :::: Organizationally, I'm now wondering whether we need separate articles on [[cardinality]] and [[cardinal number]]. What should go in which article? Also, as you say, many properties of aleph-0 can best be treated in a more general article, either on cardinal numbers or more specifically on the aleph-numbers. That begs the question, do we need a separate article on Aleph-0 at all? -- [[User:Jitse Niesen|Jitse Niesen]] 17:45, 19 June 2009 (UTC) |

## Revision as of 17:45, 19 June 2009

## 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."

- "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

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**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)

- Thanks, I did not check for links, and I wanted to avoid a "See this article" for stylistic reasons.

- Ah, so that is why you wrote "traditionally". That confused me. I see your point, but the article on Paris also starts with "Paris is the capital of France", even though one could also see "Paris" as an arbitrary name, which can even refer to other things (Greek hero, various cities in the US). I think it would be over the top to write "Paris is a string of letters which often refers to the current capital of France." But going back to this article, would you prefer it if we wrote "aleph-0 denotes …" instead of "aleph-0 is …"?

- You are right that the "see this article" looks weird, so I removed it again. Let's hope that the bold font is enough to attract attention to the link.

- Organizationally, I'm now wondering whether we need separate articles on cardinality and cardinal number. What should go in which article? Also, as you say, many properties of aleph-0 can best be treated in a more general article, either on cardinal numbers or more specifically on the aleph-numbers. That begs the question, do we need a separate article on Aleph-0 at all? -- Jitse Niesen 17:45, 19 June 2009 (UTC)