
IFF, Iff or iff can stand for: * Interchange File Format - a computer file format introduced by Electronic Arts * Identification friend or foe - a battlefield identification system * iff - the mathematics concept if and only if
:''For other possible meanings of "iff", see IFF.'' In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for "if and only if". Although "P iff Q" is most standard, common alternative phrases include "Q is necessary and sufficient for P" and "P precisely if Q". ==If and only if== ===Notation=== The corresponding logical symbols are "↔" and "⇔", and "triple bar". These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the former, ↔, is used as a symbol in logic formulas, while the latter, ⇔, is used in reasoning about those formulas (e.g., in metalogic). ===Proofs=== In most logical systems, one Proof theory a statement of the form "P iff Q", through the more roundabout route of separately proving both of the statements "if P, then Q" and "if Q, then P". (or its contrapositive, "If not P, then not Q"). Proving this pair of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. An alternative is to prove the disjunction "(P and Q) or (not-P and not-Q)", which itself can be inferred directly from either of its disjuncts--that is, because "iff" is truth-functional, "P iff Q" follows if P and Q have both been shown true, or both false. ===Origin of the abbreviation=== The abbreviation appeared in print for the first time in John Kelley's 1955 book General Topology. Its invention is often credited to the mathematician Paul Halmos, but in his autobiography he states that he borrowed it from puzzlers. ==The difference between "if" and "iff"== Put simply, the difference between ''if'' and ''iff'' can be explained with the following two sentences: # Madison will eat pudding ''if'' the pudding is a custard. (equivalently: If the pudding is a custard, then Madison will eat it) #: # Madison will eat pudding ''if and only if'' (iff) the pudding is a custard. Sentence (1) states only that Madison will eat custard pudding. It does not however preclude the possibility that Madison might also be prepared to eat bread pudding. Maybe she will, maybe she will not. The sentence does not tell us. All we know for certain is that she will not refuse custard pudding. Sentence (2) however makes it quite clear that Madison will eat custard pudding ''and custard pudding only''. She will not eat any other type of pudding. ==Advanced considerations== A sentence that is composed of two other sentences joined by "''iff''" is called a logical biconditional. ''Iff'' joins two sentences to form a new sentence. It should not be confused with logical equivalence which is a description of a relation between two sentences. The biconditional "A ''iff'' B" ''uses'' the sentences ''A'' and ''B'', describing a relation between the states of affairs ''A'' and ''B'' describe. By contrast "''A'' is logically equivalent to ''B''" mentions the two sentences: it describes a relation between those two sentences, and not between whatever matters they describe. The distinction is a very confusing one, and has led many a philosopher astray. Certainly it is the case that when ''A'' is logically equivalent to ''B'', "A ''iff'' B" is true. But the converse does not hold. Let's reconsider the sentence: :Madison will eat pudding today if and only if it's custard. There is clearly no logical equivalence between the two halves of this particular biconditional. For more on the distinction, see W. V. Quine's ''Mathematical Logic'', Section 5. In philosophy and logic, "iff" is used to indicate definitions, since definitions are supposed to be universal quantification biconditionals. In mathematics, however, the word "if" is often used in definitions, rather than "iff". This is usually for convenience, and some authors explicitly indicate that the "if" of a definition means "iff"! Here are some examples of true statements that use "iff" - true biconditionals (the first is an example of a definition): *A person is a bachelor ''iff'' that person is an unmarried but marriageable man. *"Snow is white" (in English) is true ''iff'' "''Schnee ist weiß''" (in German) is true. *For any ''p'', ''q'', and ''r'': (''p'' & ''q'') & ''r'' iff ''p'' & (''q'' & ''r''). (Since this is written using variables and "logical and", the statement would usually be written using "↔", or one of the other symbols used to write biconditionals, in place of "iff"). Other words are also sometimes emphasized in the same way by repeating the last letter; for example ''orr'' for "Or and only Or" (the exclusive disjunction). ==More general usage== ''Iff'' is used outside the field of logic, as well, in mathematics publications and talks in general. It has the same meaning as above: it is an abbreviation for ''if and only if'', indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon. (However, as noted above, ''if'', rather than ''iff'', is generally used in statements of definition.) Logic Mathematical terminology
Someone should add the triple bar to the standard symbols for "iff." But I don't know how to do so. ---- # Mary will eat pudding ''if'' it is custard. Does this sentance need wikilinks really? Does pudding and Custard have anything at all to do with this article? I think not personally. -- User: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. - User:Ledge 11:18, 18 Aug 2003 (UTC) : well... since it's symmetric, it doesn't really matter that much does it? -- User: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) ---- User: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 English 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. — user:Toby Bartels, Tuesday, June 18, 2002 : The priest-bachelor statement is is a prime example of Imprecise language... ;-) user: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? User: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. User:Delirium 18:55 12 Jun 2003 (UTC) ---- currently, Necessary and sufficient redirects to Iff. User: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. --User: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 -- User: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. user: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? -- User:Tillwe 00:31, 26 Jan 2004 (UTC) ---- = 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? -- User:Dominus 05:39, 10 May 2004 (UTC) == Possibly useful references == * [http://mathforum.org/epigone/math-history-list/hoikandther/v02140b08b25141c8b130@%5B130.58.86.135%5D] * [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. User:WmahanUser talk:Wmahan 17:56, 2004 Aug 31 (UTC) :Yes; that is conventional usage among mathematicians (I don't know about philosophical logicians, though). User:Michael Hardy 20:55, 31 Aug 2004 (UTC) Thanks. It appears to be used in logic as well (e.g. [http://www.philosophy.stir.ac.uk/staff/pritchard/71C4%20Logic/Handout2.html]), so I'll add it to the article. User:WmahanUser talk:Wmahan 06:34, 2004 Sep 1 (UTC) I think the phrase "exactly when" is common also. -- User:Dominus 02:59, 2 Sep 2004 (UTC) == Orr? == I don't know about you, but I see "orr" and Acorn RISC Machine an imperative-logic "p' := q or r". Does anybody use "orr" for the exclusive disjunction rather than "xor"? --User: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. —User:Msh210 17:03, 9 Nov 2004 (UTC) I still think so; what do you all think?User:Msh210 —User:Msh210 19:40, 15 Nov 2004 (UTC) Done.User:Msh210 —User: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. -- User: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"). --User: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. -- User:Dominus 12:57, 8 Jun 2005 (UTC)
See other meanings of words starting from letter:
Words begining with Iff:
IFF
Iff
Iff
IFF-16SV
IFF-8SVX
IFF-ILBM
Iffel_tower
Iffix_Santaph
Iffland-Ring
Iffley
Iff_(disambiguation)
IFF
IFF, Iff or iff can stand for: * Interchange File Format - a computer file format introduced by Electronic Arts * Identification friend or foe - a battlefield identification system * iff - the mathematics concept if and only if
Iff
:''For other possible meanings of "iff", see IFF.'' In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for "if and only if". Although "P iff Q" is most standard, common alternative phrases include "Q is necessary and sufficient for P" and "P precisely if Q". ==If and only if== ===Notation=== The corresponding logical symbols are "↔" and "⇔", and "triple bar". These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the former, ↔, is used as a symbol in logic formulas, while the latter, ⇔, is used in reasoning about those formulas (e.g., in metalogic). ===Proofs=== In most logical systems, one Proof theory a statement of the form "P iff Q", through the more roundabout route of separately proving both of the statements "if P, then Q" and "if Q, then P". (or its contrapositive, "If not P, then not Q"). Proving this pair of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. An alternative is to prove the disjunction "(P and Q) or (not-P and not-Q)", which itself can be inferred directly from either of its disjuncts--that is, because "iff" is truth-functional, "P iff Q" follows if P and Q have both been shown true, or both false. ===Origin of the abbreviation=== The abbreviation appeared in print for the first time in John Kelley's 1955 book General Topology. Its invention is often credited to the mathematician Paul Halmos, but in his autobiography he states that he borrowed it from puzzlers. ==The difference between "if" and "iff"== Put simply, the difference between ''if'' and ''iff'' can be explained with the following two sentences: # Madison will eat pudding ''if'' the pudding is a custard. (equivalently: If the pudding is a custard, then Madison will eat it) #: # Madison will eat pudding ''if and only if'' (iff) the pudding is a custard. Sentence (1) states only that Madison will eat custard pudding. It does not however preclude the possibility that Madison might also be prepared to eat bread pudding. Maybe she will, maybe she will not. The sentence does not tell us. All we know for certain is that she will not refuse custard pudding. Sentence (2) however makes it quite clear that Madison will eat custard pudding ''and custard pudding only''. She will not eat any other type of pudding. ==Advanced considerations== A sentence that is composed of two other sentences joined by "''iff''" is called a logical biconditional. ''Iff'' joins two sentences to form a new sentence. It should not be confused with logical equivalence which is a description of a relation between two sentences. The biconditional "A ''iff'' B" ''uses'' the sentences ''A'' and ''B'', describing a relation between the states of affairs ''A'' and ''B'' describe. By contrast "''A'' is logically equivalent to ''B''" mentions the two sentences: it describes a relation between those two sentences, and not between whatever matters they describe. The distinction is a very confusing one, and has led many a philosopher astray. Certainly it is the case that when ''A'' is logically equivalent to ''B'', "A ''iff'' B" is true. But the converse does not hold. Let's reconsider the sentence: :Madison will eat pudding today if and only if it's custard. There is clearly no logical equivalence between the two halves of this particular biconditional. For more on the distinction, see W. V. Quine's ''Mathematical Logic'', Section 5. In philosophy and logic, "iff" is used to indicate definitions, since definitions are supposed to be universal quantification biconditionals. In mathematics, however, the word "if" is often used in definitions, rather than "iff". This is usually for convenience, and some authors explicitly indicate that the "if" of a definition means "iff"! Here are some examples of true statements that use "iff" - true biconditionals (the first is an example of a definition): *A person is a bachelor ''iff'' that person is an unmarried but marriageable man. *"Snow is white" (in English) is true ''iff'' "''Schnee ist weiß''" (in German) is true. *For any ''p'', ''q'', and ''r'': (''p'' & ''q'') & ''r'' iff ''p'' & (''q'' & ''r''). (Since this is written using variables and "logical and", the statement would usually be written using "↔", or one of the other symbols used to write biconditionals, in place of "iff"). Other words are also sometimes emphasized in the same way by repeating the last letter; for example ''orr'' for "Or and only Or" (the exclusive disjunction). ==More general usage== ''Iff'' is used outside the field of logic, as well, in mathematics publications and talks in general. It has the same meaning as above: it is an abbreviation for ''if and only if'', indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon. (However, as noted above, ''if'', rather than ''iff'', is generally used in statements of definition.) Logic Mathematical terminology
Iff
Someone should add the triple bar to the standard symbols for "iff." But I don't know how to do so. ---- # Mary will eat pudding ''if'' it is custard. Does this sentance need wikilinks really? Does pudding and Custard have anything at all to do with this article? I think not personally. -- User: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. - User:Ledge 11:18, 18 Aug 2003 (UTC) : well... since it's symmetric, it doesn't really matter that much does it? -- User: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) ---- User: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 English 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. — user:Toby Bartels, Tuesday, June 18, 2002 : The priest-bachelor statement is is a prime example of Imprecise language... ;-) user: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? User: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. User:Delirium 18:55 12 Jun 2003 (UTC) ---- currently, Necessary and sufficient redirects to Iff. User: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. --User: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 -- User: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. user: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? -- User:Tillwe 00:31, 26 Jan 2004 (UTC) ---- = 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? -- User:Dominus 05:39, 10 May 2004 (UTC) == Possibly useful references == * [http://mathforum.org/epigone/math-history-list/hoikandther/v02140b08b25141c8b130@%5B130.58.86.135%5D] * [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. User:WmahanUser talk:Wmahan 17:56, 2004 Aug 31 (UTC) :Yes; that is conventional usage among mathematicians (I don't know about philosophical logicians, though). User:Michael Hardy 20:55, 31 Aug 2004 (UTC) Thanks. It appears to be used in logic as well (e.g. [http://www.philosophy.stir.ac.uk/staff/pritchard/71C4%20Logic/Handout2.html]), so I'll add it to the article. User:WmahanUser talk:Wmahan 06:34, 2004 Sep 1 (UTC) I think the phrase "exactly when" is common also. -- User:Dominus 02:59, 2 Sep 2004 (UTC) == Orr? == I don't know about you, but I see "orr" and Acorn RISC Machine an imperative-logic "p' := q or r". Does anybody use "orr" for the exclusive disjunction rather than "xor"? --User: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. —User:Msh210 17:03, 9 Nov 2004 (UTC) I still think so; what do you all think?User:Msh210 —User:Msh210 19:40, 15 Nov 2004 (UTC) Done.User:Msh210 —User: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. -- User: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"). --User: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. -- User:Dominus 12:57, 8 Jun 2005 (UTC)
See other meanings of words starting from letter:
I
IA | IB | IC | ID | IE | IF | IG | IH | IJ | IK | IL | IM | IN | IO | IP | IR | IS | IT | IU | IW | IX | IY | IZ |Words begining with Iff:
IFF
Iff
Iff
IFF-16SV
IFF-8SVX
IFF-ILBM
Iffel_tower
Iffix_Santaph
Iffland-Ring
Iffley
Iff_(disambiguation)
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