Talk:Iff
From Academic Kids
Someone should add the triple bar to the standard symbols for "iff." But I don't know how to do so.
Does this sentance need wikilinks really? Does pudding and Custard have anything at all to do with this article? I think not personally. -- 82.3.32.75 13:32, 21 Feb 2005 (UTC)
The equivalent of 'P is necessary and sufficient for Q' would be 'Q iff P' (not 'P iff Q') would it not? I've also wikilinked necessary and sufficient. - Ledge 11:18, 18 Aug 2003 (UTC)
- well... since it's symmetric, it doesn't really matter that much does it? -- Tarquin 11:38, 18 Aug 2003 (UTC)
Gosh, so it is. How have I lived so long without realising that?
- it should be symmetric, but the example below, which should show the difference between the equivalence and iff is not symmetric - actually the second part of the sentence (it's custart) is not even a sentence! This example is basicly wrong and it seems that the discusion of the mentioned difference is some (maybe polemic) lingual issue, but no logical nor mathematical, which (in this case) is the same. (Jester (not yet a user) 2:50, 9 Sep 2004)
Ark: Yes, a priest is a bachelor, at least as I understand the term. The Oxford English Dictionary says only that the man must be of marriageable age, which is arguably included in the term "man". Every American dictionary that I can find on the Net gives our original definition, possibly adding that age is irrelevant. If you have support for your definition, then I'd like to hear it; otherwise, I suggest returning the definition to what it was. OTOH, if controversy remains, we might look for a different definition to use. — Toby Bartels, Tuesday, June 18, 2002
- The priest-bachelor statement is is a prime example of Imprecise language... ;-) Tarquin, Tuesday, June 18, 2002
well, to my naive surprise, this is the necessary and sufficient article. But it doesn't go into the terms necessary and sufficient...or am I missing something? Kingturtle 02:35 Apr 18, 2003 (UTC)
- Well, I'm not sure. This is the iff article. It isn't clear it should go into the terms necessary and sufficient. But at the very least, necessary and sufficient are normally used in the sense of necessary condition and sufficient condition--I take it that's what you want. But the conjunction of those two is logical equivalence, which is not the same as iff (as explained in the article).
There was some confusing equivocation between use and mention here--between the biconditional, which is a connective and logical equivalence, which is a relation. I tried to clear it up, but it's a knotty topic.
- I'm not sure the current version doesn't "clear it up" too much in the opposite direction. There is a distinction sometimes, but often there is not in fact a distinction, and many formal logics use a single symbol to indicate both, not the two separate symbols (single- and double-barred <->) used in this article. Delirium 18:55 12 Jun 2003 (UTC)
currently, Necessary and sufficient redirects to Iff. Kingturtle 02:46 Apr 18, 2003 (UTC)
- I realized that, a bit later. I've written a brief article on it and eliminated the redirection. hope its helpful
I'm not sure I like the "iff is not equivalence" example:
- Mary will eat pudding today if and only if it's custard.
I think this actually is a case of equivalence, that is being muddled by the phrasing. What we're saying is "(Mary will eat pudding today) iff (The pudding today is a custard)". Thus the logical statements "Mary will eat pudding today" and "The pudding today is a custard" are in fact equivalent: they have identical truth tables. So I still don't see the discrepancy. --Delirium 22:58 12 Jul 2003 (UTC)
- I think you're right. It's bringing the meaning of the words into the matter, which is wrong -- Tarquin 10:19 13 Jul 2003 (UTC)
Regarding "if/iff" convention for defs:
I've reinserted the comment about "if" being used conventionally in math defs. I'm sorry, I've read a lot of math books, and this is a common convention. Many definitions use the terminology "if", in the sense of "If P(X), then X is called blah" or "X is said to be blah if P(X)", yet not every definition uses "iff", and all definitions are intended to be "iff", because that's what definitions are. (To counter your remark, definitions are not intended to assert equivalencies; an equivalence is usually meant to indicate a statement saying two things imply each other that has to be PROVED...definitions aren't proved, they're declared, so it doesn't make sense to say e.g. "'R is an integral domain' is equivalent to 'R is a commutative ring with identity'" because these statements aren't "equivalent" in the ordinary sense of the term, one does not PROVE they're equivalent, that simply IS the definition of an integral domain. Here are several cases where the "if" convention is used in the wikipedia itself...
- "A prime p is called primorial or prime-factorial if it has the form p = Π(n) ± 1 for some number n" (from prime number)
- "If a divides b and b divides a, then we say a and b are associated elements. a and b are associated if and only if there exists a unit u such that au = b." (from integral domain...notice, the first use of the word is in the sense of a definition, hence only "if" is used (although "iff" would be correct as well), but the second IS an actual theorem (result) because the equivalent condition requires proof. So, for the second statement, the meaning would change if "iff" were replaced by "if", although for the first statement it doesn't matter.
- "In complex analysis, a function is called entire if it is defined on the whole complex plane and is holomorphic everywhere" (from entire function).
The list could go on. Revolver
Im confused by the
- A person is a bachelor iff that person is an unmarried but marriagable man.
example -- there could be unmarried but marriagable men (not only the priests mentioned above), for example widowers. I wouldn't think they are bachelors (are they?). If not, the (P iff Q) Q->P direction isn't true. And what about bachelor being also a term for an university diploma? Is "Tom did his B.A. well and is now a Bachelor" a correct English sentence? And what about a marriaged Tom that is a Bachelor in this sense? Would he destroy the iff above? -- till we *) 00:31, 26 Jan 2004 (UTC)
| Contents |
Coinage of "iff" by Kelley / Halmos
The article says:
- The abbreviation appeared in print for the first time in John Kelley's 1955 book General Topology.
However, the preface of the 1955 edition of General Topology says
- In some cases where mathematical content requires "if and only if" and euphony demands something less I use Halmos' "iff".
which suggests that he did get it from Halmos. Now Kelley did know Halmost personally so it's possible that this was the first appearance of "iff" in print. But it seems more likely that Kelley saw it in some paper of Halmos'. I can't think of any way to pursue this any further, other than to ask Halmos. (Kelley died in 1999.) Does anyone have any other suggestions? -- Dominus 05:39, 10 May 2004 (UTC)
Possibly useful references
- [1] (http://mathforum.org/epigone/math-history-list/hoikandther/v02140b08b25141c8b130@%5B130.58.86.135%5D)
- [2] (http://mathforum.org/epigone/math-history-list/yexspimpclin/s62e29a2.024@scu.edu)
"Precisely if"
Does the phrase "precisely if" mean the same thing as iff? If so, it could be added to the article. Wmahan. 17:56, 2004 Aug 31 (UTC)
- Yes; that is conventional usage among mathematicians (I don't know about philosophical logicians, though). Michael Hardy 20:55, 31 Aug 2004 (UTC)
Thanks. It appears to be used in logic as well (e.g. [3] (http://www.philosophy.stir.ac.uk/staff/pritchard/71C4%20Logic/Handout2.html)), so I'll add it to the article. Wmahan. 06:34, 2004 Sep 1 (UTC)
I think the phrase "exactly when" is common also. -- Dominus 02:59, 2 Sep 2004 (UTC)
Orr?
I don't know about you, but I see "orr" and think of an imperative-logic "p' := q or r". Does anybody use "orr" for the exclusive disjunction rather than "xor"? --Damian Yerrick 08:23, 6 Sep 2004 (UTC)
Organization
I wrote in Talk:Mathematical jargon, in part:
- Iff has two uses, imho. One is used in logic (and related fields, I suppose) to mean a binary function from a theory to a truth-value set
iff : Th x Th → {T,F}
- and the other is used in arguments in any math paper or lecture. The meanings are the same, I think, but the uses are different. I think that Iff should be edited to reflect these two uses; right now it blends them. —msh210 17:03, 9 Nov 2004 (UTC)
I still think so; what do you all think? —msh210 19:40, 15 Nov 2004 (UTC)
Done. —msh210 18:57, 17 Nov 2004 (UTC)
"P iff Q" not equal to "P is necessary and sufficient for Q"
In my opinion, there is a little mistake in this article... I think it should be vice versa: "P iff Q" means "Q is neseccary and sufficient for P" instead of "P is necessary and sufficient for Q" isn't it?
- Both are equally correct. -- Dominus 01:27, 6 Jun 2005 (UTC)
- Yeah, although the suggested change does match up a little better with colloquial English usage ("P if Q" means "Q is sufficient for P", and "P only if Q" means "Q is necessary for P", so "P iff Q" means "Q is necessary and sufficient for P"). --Delirium 03:03, Jun 8, 2005 (UTC)
- "P if Q" also means that P is necessary for Q, and "P only if Q" means that P is sufficient for Q. Thus, "P iff Q" means "P is necessary and sufficient for Q". I repeat, both are equally correct. -- Dominus 12:57, 8 Jun 2005 (UTC)
