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Talk:Bounded quantifier

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Hard to Understand

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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 (talkcontribs) 21:32, 5 April 2009 (UTC)[reply]

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

Edits

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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)[reply]

Isn't every quantifier bounded?

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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)[reply]

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)[reply]