Talk:Bounded quantifier

Hard to Understand

Came here to look for a quick definition of "bounded quantifier" which is obviously absent from this article.

the article says "There are two bounded quantifiers: \forall n < t and \exists n < t. These quantifiers bind the number variable n and contain a numeric term t which may not mention n but which may have other free variables."

It's quite apparent that here "<" do not mean less than... but what do they mean? furthermore, it says "These quantifiers bind the number"... what does it mean to bind something?

I think the article needs some very basic definitions. for example: —Preceding unsigned comment added by Philosophy.dude (talk • contribs) 21:32, 5 April 2009 (UTC)

Yes, the < means less than. — Carl (CBM · talk) 02:48, 6 April 2009 (UTC)

yeah i figured the stuff out from a book... still, why does the article say "there are TWO bounded quantifiers" ? it makes it sound like /forall n > t and /exists n > t are NOT bounded quantifiers...

I get that "/forall n > t" may not be useful as "/forall n < t", but shouldn't they be counted as well, and thus makes it FOUR basic kinds of bounded quantifiers? "/forall n > t", "/forall n < t", "/exists n > t", "/exists n < t"?

Philosophy.dude (talk) 02:53, 9 April 2009 (UTC)

There are two (forall and exists) in each context. And there are two basic contexts in which they are used: arithmetic and set theory. The type you are writing (forall x > 0 ...) are really just a special case of the bounded quantifiers in set theory, and are not particularly related to the bounded quantifiers in arithmetic, even though they have a > sign in them. — Carl (CBM · talk) 02:58, 9 April 2009 (UTC)

I already get the whole business about bounded quantifiers (it's not that hard), and the article makes perfect sense now. However the problem is that i think the article would make perfect sense only to someone who already know what in the world a bounded quantifier is...

i'm gonna try adding a few word to itPhilosophy.dude (talk) 03:06, 9 April 2009 (UTC)

Edits

The "otheruses4" template is more specific about which hatnote is intended, while "about" is more vague about what is supposed to be generated. Moreover, "Some examples" seems like redundant writing: of course the list only has "some" examples, but what benefit is there in using the word "some"? It makes the prose sound less polished, without adding any additional information. — Carl (CBM · talk) 22:48, 15 April 2017 (UTC)

Isn't every quantifier bounded?

I can't understand what difference bounded actually makes. As the article Quantifier (logic) states: "Every quantification involves one specific variable and a domain of discourse or range of quantification." So isn't every quantifier bounded? St.nerol (talk) 10:31, 17 February 2021 (UTC)

Good question. The short answer is that unbounded quantifiers range over the entire universe, the bounded ones are specifically restricted to a subset/subclass of the universe. The long answer is that I don't know how to say this more formally, so I reposted your question to Talk:Quantifier (logic)#Sharpen distinction w.r.t. bounded quantifier. Maybe someone over there will notice and answer. 67.198.37.16 (talk) 20:39, 28 November 2023 (UTC)