Talk:Quantification

From Wikipedia, the free encyclopedia

1 Old material
2 New intro
3 Attention banner needed?
4 Uniform vs pointwise continuity

[edit] Old material

This contains material from Universal quantification and Existential quantification. When I finish transferring items (tomorrow?), then I'll remove stuff from those articles that applies to quantification in general and appears here. Then those articles can focus on aspects unique to their particular sort of quantification. For now, those articles remain complete, without relying on this one. -- Toby Bartels 10:30, 31 Jul 2003 (UTC)

These changes have now been made. -- Toby Bartels 21:29, 3 Aug 2003 (UTC)

This is a important article; it was well written but I think some clarification on the rule of formation would be helpful. However, I believe in the scientific method. TEAR IT APART. After all, I'm just a vacuum cleaner.CSTAR 03:56, 12 May 2004 (UTC)

I have continued to make some changes to discuss natural language quantification, informal mathematical quantification and the formal semantics of quantification (at least what is objective quantifcation, as opposed to substitute quantification). Again I think a lot can be removed. Please have a look at this and modify. CSTAR 05:42, 15 May 2004 (UTC)

I will add some stuff on multal and paucal quantification ( quantification such as for almost every x blah...) and then I'll call it quits on this article.

Could we merge the other articles on existential and universal quantification into this one?CSTAR 23:12, 15 May 2004 (UTC)

[edit] New intro

The new intro is innaccurate. Quantification is not limited to size. Unless there is any objection soon I will revert it.CSTAR 14:03, 19 Nov 2004 (UTC)

Your change is sound, in that what you have written is better than what you replaced, but I've got some reservations about the way the relation between quantifiers and quantities is being treated. I'm not a linguist, and am not entirely comfortable with the following material, but it seems to me that in natural language, mass noun (eg. two pints of beer) and count noun constructions (eg. four cats) are in many respects the paradigmatic instances of quantifiers, with some, no and all being more in the line of special instances. It seems backwards to me to relegate the quantity-related aspects of quanitifers to the back seat. ---- Charles Stewart 14:18, 19 Nov 2004 (UTC)

Sigh, yes, I have to agree with your assertion:

I've got some reservations about the way the relation between quantifiers and quantities is being treated.

In fact the article's treatment of quantification is almost entirely restricted to quantification in formal languages (Mea culpa). Unfortunately, I don't know much about this, I admit. When I first stumbled on this page it only dealt with formal quantification and moreover even with that restricted focus, I thought the material was not very informative and in fact a little condescending to the reader.

Of course feel free to revert back to any previous state or some suitable middle.

Sooner or later I will tackle this problem. I can't think of a 30 second edit that will resolve the issue, and I have little time for WP right now, so I am OK with leaving it as is. ---- Charles Stewart 23:29, 20 Nov 2004 (UTC)

[edit] Attention banner needed?

Should we put in an attention banner? Yes, I now have pangs of guilt about this article. Please, someone, absolve me of the burden of this guilt. CSTAR 15:29, 19 Nov 2004 (UTC)

No guilt feelings are deserved. What is an attention banner? ---- Charles Stewart 23:29, 20 Nov 2004 (UTC)

The following is an attention banner:

CSTAR 23:33, 20 Nov 2004 (UTC)

[edit] Uniform vs pointwise continuity

Let f be a real-valued function on R.

A: Pointwise continuity of f on R:

$\forall x \in \mathbb{R}, \ \forall \epsilon >0, \exists \delta > 0, \forall h \in \mathbb{R}, \quad |h| < \delta \implies |f(x) - f(x+h)| < \epsilon$

which is the same as

A': Pointwise continuity of f on R:

$\forall \epsilon >0, \ \forall x \in \mathbb{R}, \exists \delta > 0, \ \forall h \in \mathbb{R}, \quad |h| < \delta \implies |f(x) - f(x+h)| < \epsilon$