# Is "iff" considered a real word or just an abbreviation?

I wonder if "iff" is considered a real word (as LEO says) or is it just an abbreviation (as in Wiktionary)?

• Does this have anything to do with today's XKCD? Commented Mar 23, 2012 at 7:47
• @Jim Yes. You got me. Commented Mar 23, 2012 at 7:51
• It’s considered an abomination. [If you find that writing “if and only if” is too long, use the proper symbol, i.e. “↔”] Commented Mar 23, 2012 at 11:12
• @Konrad: For those writing metalogical statements, "↔", "⇔", and "iff" work at different levels and all three are needed. "A ↔ B ⇔ ((A ∧ B) ∨ ~(A ∨ B)) iff our definitions follow standard propositional semantics." ↔ is used as a truth function, ⇔ is used as equivalence, and iff is used to explain the conditions when the equivalence holds.
– user2400
Commented Mar 23, 2012 at 12:28
• @Konrad, specifically who considers it an abomination? That's a strong statement, and I think there are many, many people who would disagree. Are you referring specifically to usage outside of mathematics? Commented Mar 23, 2012 at 16:14

## 7 Answers

I would count it as jargon and I'd never use it in prose. It's a programming/maths term meaning if and only if and should be restricted to circles where it's likely to be understood (edit like XKCD ).

The question of whether it's an abbreviation is interesting. It's obviously shorter than "if and only if" but I think I'd say it was a more of a symbol. Perhaps that's my programming background coming out [where symbol has a particular meaning (see number 2 here)]. However as it consists of more than one recognisable letter, it might be better to say it's an abbreviation

Here's an Ngram which shows that iff has become more popular recently, corresponding to the increase in computing. That may explain the increase in "if and only if" as well. I have no idea whether the incidence around 1800 is simply an alternative spelling of if or whether that actually meant "if and only if".

• It is not (only) a programming term, however. More of a logic term, I would say. Commented Mar 23, 2012 at 8:26
• You're right, as today's XKCD indicates. But I'm not an expert in formal logic. And not an expert programmer either(!) but that's where my experience lies. Commented Mar 23, 2012 at 8:33
• @Eyvind More a maths and logic term. Often used in mathematical proofs (often the proof is to prove the "iff" in a statement). Commented Mar 23, 2012 at 11:44
• Philosophy, math, CS, ling, engin, they all use it. But never in speech. There is no special pronunciation difference between iff and if, so it couldn't be used in speech. It's strictly in informal writing (handouts, blackboard, notes, blogs, letters, etc.) Commented Mar 23, 2012 at 17:15
• @JohnLawler Actually there is an important (critical) distinction in how `if` and `iff` are pronounced: `if` is pronounced "if", and `iff` is pronounced "if and only if" - In the context of formal logic they have substantially different meanings. `iff` is a generally accepted abbreviation in the Mathematics and Computer Science fields (and probably others that invoke formal logic), but it is definitely an abbreviation/shorthand, not a word. Commented Mar 23, 2012 at 18:40

While acknowledging the excellent answer from @Andrew Leach, one man's jargon is another man's specialized terminology. To the non-mathematician, this is jargon. To the logician, this is an abbreviation that is used in a similar way (though not as frequently) as QED. (At the bottom of a proof, a mathematician will write QED, standing for quod erat demonstrandum, to indicate that he or she has proven that which was set out to be proven.) You may find QED in popular usage, but it is both specialized terminology and an abbreviation.

I first ran across IFF in my 8th grade algebra class, and it was used in logic truth tables. It meant, as others have correctly stated, "If-and-only-if."

In the context of the XKCD comic, it means Honk if (and only if) you love formal logic. The truth table would be:

``````You love              You honk           You obey the
formal logic                             bumper sticker
Yes                   Yes                Yes
No                    No                 Yes
Yes                   No                 No
No                    Yes                No
``````

This means that if you honk because the driver swerved into your lane, then you are not obeying the bumper sticker (or the truth value of the bumper sticker's logical statement). And if you don't honk even though you love formal logic, then you're not obeying the truth value of the bumper sticker.

My experience in both programming and math has seen IFF rarely in programming and sometimes in math and logic. Few programmers, for instance, would recognize the equivalence between ~ XOR (not Exclusive OR operation) and IFF.

Q.E.D., but IFF you understood the truth table.

• +1 This is a great explanation of iff, although it's not good driving advice at all.
– J.R.
Commented Mar 23, 2012 at 14:25
• Also, writing Q.E.D. at the end of proofs is a bit unfashionable these days. The current fashion is to draw a little black box, sometimes called a 'tombstone'. Commented Mar 23, 2012 at 16:58
• My profs would sometimes use the "Therefore" sign (U+2234 or ∴) at a conclusion, and in place of QED; this was more for lemmas than proofs. I will not dispute "unfashionable." My exposure to QED and IFF were back in the day when "high tech" meant a K&E slide rule or a four-function calculator. Commented Mar 23, 2012 at 17:32

OED 1971 doesn't list iff at all. The American Heritage Dictionary of the English Language, Fourth Edition says it's an abbreviation. Difficult to consider it a real word when it's normally pronounced as three separate letters.

• Oh, and the New Zealand Oxford Dictionary (2005) lists iff, but doesn't label it as an abbreviation. In my opinion, it's wrong not to do so.
– user16269
Commented Mar 23, 2012 at 8:02
• The online version of the OED has it and defines it as "A written form of abbreviation of the phrase ‘if and only if’, always read as ‘if and only if’, used in Math. and Logic to introduce a condition that is necessary as well as sufficient, or a statement that is implied by and implies the preceding one.'" Commented Mar 23, 2012 at 8:08
• It's normally pronounced as for different words.
– Hugo
Commented Mar 23, 2012 at 8:25
• Fair enough then. When I studied logic, the lecturers always said "if and only if". They only said "I. F. F." when introducing the notation for the first time.
– Hugo
Commented Mar 23, 2012 at 8:33
• @David: in my experience, this abbreviation is pronounced "if and only if" in the same way etc is pronounced "et cetera". That in your experience it's pronounced "I F F" is interesting, but doesn't make one more valid than the other. Commented Mar 23, 2012 at 9:43

Re: is iff a word, or an abbreviation?

Does it need to be one or the other? It doesn't seem to be either one, in a pure sense.

I'm more comfortable identifying it as shorthand for "if and only if".

Dictionaries specifically relate the word shorthand to the standardized system of stenography, but many also list a secondary definition, something along the lines of "an abbreviated or shortened way of communicating something."

Wear the shoe iff it fits... In this case, I think shorthand fits better than either abbreviation or word.

Although I had expected recent dictionaries to agree unanimously that iff is primarily an abbreviation, I found that is not the case. On the one hand (consistent with user16269's answer from 2012), The American Heritage Dictionary of the English Language, fifth edition (2011) has this entry for (lowercase) iff:

iff abbr. if and only if

AHDEL also has an entry for uppercase IFF:

IFF abbr. identification, friend or foe

So AHDEL and the OED (as reported in Greybeard's recent answer) assert that iff is to be understood fundamentally as an abbreviation.

Merriam-Webster's Eleventh Collegiate Dictionary (2003), however, takes a different view. Here are its entries for iff and IFF:

iff conj \ˈif-ᵊn(d)-ˈōn-lē-ˌif; ˈif, sometimes read with a prolonged f\ conj {alter. of [conjunctive] if} (1955) : if and only if <two figures are congruent iff one can be placed over the other so that they coincide>

IFF abbr identification, friend or foe

In its "Explanatory Notes" section, the Eleventh Collegiate remarks that its functional labels are not limited to traditional parts of speech:

Other italicized labels used to indicate functional classifications that are not traditional parts of speech are: geog abbr [other labels omitted]

To the untrained eye (mine), MW's treatment of abbreviated forms appears to be unpredictably arbitrary. For example, it identifies SUV as a noun (equivalent to sports utility vehicle) but categorizes SVGA as an "abbr" (for "super video graphics array"); and it identifies SWAK" as an "abbr" (for "sealed with a kiss") but treats WYSIWIG as a noun (based on "what you see is what you get," but with a distinct nominal meaning). The consistent logic underlying these various decisions is difficult to discern.

Incidentally, MW's first occurrence date of 1955 for iff in the relevant sense is subject to revision. Multiple Google Books sources attribute the short form of the expression to the mathematician Paul Halmos, although I haven't found a source that identifies the particular text in which he introduced it. The notation certainly goes back at least to 1950. From William Feller, An Introduction to Probability Theory and Its Applications, volume 2 (1950):

Iff is an abbreviation for if and only if.

Personally, I don't really care if it's listed or not.

IFF is, as far as I know, an established contraction of if and only if in engineering, physics, philosophy (I believe the first experience I had with IFF was when our philosophy professor used it), and as I recall in mathematics as well. Some people are snarky about it, some aren't. I use it all the time. I've seen it used in all the areas above over the past three or four decades.

Perhaps not definitively a "word" in the spoken sense. but a "working" word or defacto written word? Yes, pretty much.

"Iff" is classed an abbreviation by OED

A written form of abbreviation of the phrase ‘if and only if’, always read as ‘if and only if’, used in Mathematics and Logic to introduce a condition that is necessary as well as sufficient, or a statement that is implied by and implies the preceding one.

1955 J. L. Kelley Gen. Topol. vii. 232 F is equicontinuous at x iff there is a neighborhood of x whose image under every member of F is small.

1971 G. Hunter Metalogic 16 Hereafter we abbreviate ‘if and only if’ to ‘iff’.

1972 Royal Inst. Philos. Lect. V. 34 An integer n is prime iff the only integers which divide it without remainder are itself and one.

However, it operates as a preposition.