Talk:Number

blackboard bold does not mesh well with a paragraph. Pizza Puzzle

Eh, I'm used to seeing blackboard bold; plain bold reminds me of a variable, not a set.

I agree that we should use it; however, the current font for it is too big and doesn't mesh with the rest of the page. Perhaps, if somebody submits a slightly smaller .png we can use that. Pizza Puzzle

I plan to upload a whole bunch of <.png>s like this later this month. Of course, feel free to beat me to it. ^_^ Still we should still prefer markup that renders most directly in HTML, when such a thing works -- for now. -- Toby Bartels 05:57 12 Jun 2003 (UTC)

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Could somebody produce a little Venn diagram picture showing the various number sets? I removed this verbal description of the Venn diagram. AxelBoldt 15:23, 29 Sep 2003 (UTC)

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This statement is incorrect:

"Ratios of integers are called rational numbers or fractions."

In fact, ratios of integers are fractions but NOT rational numbers. The union of the set of integers and the set of fractions equals the set of rational numbers. The distinction between integers and fractions is that no less than two integers (by ratio) are required to define a fraction.

I suspect this error has been carried over to a couple of other related pages. It must be corrected.

OmegaMan

Rationals are usually defined as equivalence classes of ordered pairs of integers. Saying that they are ratios of integers is reasonable; this is only supposed to be an informal statement. A formal construction is given in the rational number article. --Zundark 08:17, 17 Nov 2003 (UTC)

Yes but the formal construction you directed me to is for the rational numbers- NOT the fractions. The presentation of the various sets of numbers is more clearly understandable if it incorporates a brief summary of their methodical construction, one built onto the next.

Where the integers have already been defined seperately, all trivial cases of fractions which equal integers should then be eliminated as redundant (i.e., those where ratios of two integers, converted to fractions, can be simplified such that the denominator is equal to one). Then, the rationals can be defined as the union of the two underlying subsets.

Note that integers require only one integer (obviously) to define themselves reflexively which is not possible for fractions.

You may think I am splitting trivial hairs. Still, the distinction I am making is reality-based and relevant. I am not just making this stuff up as I go along. It came directly from a "theory of arithmetic" textbook I own.

OmegaMan

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This article is missing the ordinal/cardinal distinction for finite numbers. Although the finite ordinals are the same as the finite cardinals, the use to which they are put is different: "I have five beads" vs. "this is door number 5", and so they are conceptually different, even if mathematically equivalent. Can someone help put this distinction in the article? -- The Anome 13:54, 27 Jan 2004 (UTC)

Contents

1 Umpteen 1 Natural Numbers and Zero 2 Mixing Numbers & Biology 3 extensions and generalizations

Umpteen

I've added umpteen in the "see also" list, largely to de-orphan it. I'm not absolutely sure this is the right article to link to it, but I can't think of an alternative. Suggestions would be more than welcome. DavidWBrooks 20:01, 16 Feb 2004 (UTC)

Natural Numbers and Zero

I have never known zero to be included in the set of natural numbers (a.k.a. counting numbers, hence the exclusion of zero, as one never counts the zeroth member of a set). Rather, it is the only non-natural member of the set of whole numbers. I hope someone will correct this, or at least address the question if I am in error.

Arnold Karr

It's very common to include 0 as a natural number (so that "natural number" and "finite ordinal" mean the same thing). It's undesirable for some purposes, however, so not everyone does it. --Zundark 07:42, 23 May 2004 (UTC)

I think it's very natural to have zero items of something (in contrast to having a negative amount of something). In fact, all of us own zero items of almost everything. It is at least as natural as the usual definition of (the number) zero as the empty set.

Of course we do not count the zeroth member of a set, but when we count something, we start out with zero items counted, before adding the first to the inventory, if there is any. When somebody asks you to count the number of apples in your pocket, you would not protest saying "I cannot count them". You would maybe say "there are none", but this is just a synonym of zero. MFH 13:31, 7 Apr 2005 (UTC)

Mixing Numbers & Biology

I advocate the total removal of the speculative "biological basis" section, regardless of whether or not it may be wholly or partially correct. We should stick to provable information in an article involving mathematics in an online encyclopedia. OmegaMan

extensions and generalizations

The section "generalizations" should be merged into "extensions" (which could receive subsectioning). I suggest to put it after the nonstandard stuff and before the comment on abstract algebra. Please feel free to do so. MFH 18:07, 7 Apr 2005 (UTC)