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

Question

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

Answer 1

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".

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

"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.