Is the word "iff", meaning "if and only if", recognized outside of logic?

In particular, is it appropriate for a physics text? Or is this kind of abbreviation frowned upon?

  • 10
    Suggest that OP give more specifics about what kind of context is expected. Written on blackboard? Homework? Lecture notes? Thesis? Published paper? Spoken aloud? (In roughly decreasing order of acceptability.) Dec 28, 2020 at 1:56
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    – cag51
    Dec 30, 2020 at 3:10

5 Answers 5


The abbreviation iff is generally understood in several fields outside logic, and in my experience it is well understood by physicists, but the golden rule is to define every abbreviation at its first use and/or provide a list of abbreviations. In this way, even those not familiar with an abbreviation will be able to understand the text.

However, in general, abbreviations may make a text less readable and therefore should be used judiciously. Thus, ask yourself if you will have to use the expression if and only if so frequently to warrant an abbreviation, sparing you just a bunch of characters, and think whether to limit its use to e.g. theorem statements.

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    I don't agree that defining iff as an abbreviation is correct, at least in maths.
    – Jessica B
    Dec 27, 2020 at 15:52
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    @JessicaB By common definition of abbreviation —"a shortened form of a written word or phrase used in place of the whole word or phrase"—, I don't know why you wouldn't call it an abbreviation. Note also that the OP is interested in physics. Dec 27, 2020 at 15:55
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    That's a very wide definition of abbreviation, and if you're using that definition then your rule isn't really correct. For example, you would never provide as explanation of it's. Note that iff doesn't follow any standard pattern for forming an abbreviation, and also cannot be spoken aloud in the contracted form (while retaining its meaning).
    – Jessica B
    Dec 27, 2020 at 17:07
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    @JessicaB It's is part of the English language, and it's a specific form of abbreviation: it's a contraction. And one can choose abbreviations outside standard patterns. The fact that it cannot be spoken aloud is irrelevant: it just means that it's not an acronym. But also within maths, I suspect that many would agree that that is an abbreviation. E.g., here is a quotation from H. B. Enderton, Elements of Set Theory: "Also we abbreviate the phrase "if and only if" as "iff"". So, I feel you may have a too personal view of the meaning of abbreviation. Dec 27, 2020 at 17:13
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    @JessicaB I also add that iff is present in the Oxford Dictionary of English and it is exactly defined as an abbreviation: "A written form of abbreviation of the phrase ‘if and only if’". Dec 27, 2020 at 17:30

You can sort this sort of thing out by looking at papers in journals. Google speeds this along. I searched as follows:

"iff" journal die reine und angewandte mathematik


"iff" "Physical review"

to confirm that there are plenty of papers in physics and math that use "iff" without explanation. The one paper I saw that defined this was in Physical Review Letters. You might want to search similarly in one of your target journals.

However: Do think about your target audience. An experimental physicist might be confused by this abbreviation.

A nice trick is to write things with nice large figures and few abbreviations and see how long the paper is. If you are over the page limits for a journal by just a little, you start shrinking images, tightening the prose, and using the more common abbreviations. Many physics papers have way too many abbreviations so do try to not use every abbreviation possible.

Another reason to use an abbreviation or a symbol (like \Leftrightarrow) is to make a multiline-equation a single-line equation, or to make a two-column equation fit in one column. This can greatly improve the look and readability of a paper.

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    Thank you for your research. Its only for a bachelors project I'm doing, not a paper. As the page count is not limited I think I will stick to the advice given not to use too many abbreviations.
    – anon
    Dec 27, 2020 at 19:13
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    @Student0284 For a bachelors project you probably will do fine either way. Dec 27, 2020 at 20:32
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    The reason why this is defined in Physical Review Letters is very likely that Physical Review has a rather strict style guide which is usually rather strictly enforced. Acronyms have to be defined, even if they are considered to be well-known.
    – user151413
    Dec 27, 2020 at 22:31
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    This experimentalist would understand it, but probably picked up outside work from someone with a maths background. I'd use it only if really necessary, e.g. in something like a display equation that's better without wrapping
    – Chris H
    Dec 28, 2020 at 15:41
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    I doubt that anyone can get a degree in physics without taking some math classes, where they will be exposed to proofs, thus getting exposed to "iff". Dec 28, 2020 at 16:58

The use of iff outside of formal logic is shorthand, and so is only appropriate in contexts where shorthand is appropriate.

For example, it's probably fine in a piece of maths homework, may or may not be a good choice in lecture notes (depending on their style), and not suitable for a research paper (at least in pure maths).

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    The word "iff" appears in the 1995 edition of the Concise Oxford English Dictionary. The etymological note in there suggests it arose as an "extension" of "if", rather than as a "shorthand" or "abbreviation". Dec 27, 2020 at 17:18
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    I don't know what is standard in physics. However, in mathematics (outside of logic), this is the correct answer. Though it might appear in published papers sometimes, it is standard (and usually considered better) to expand shorthand like "iff" to "if and only if," in much the same way that the backwards A and E symbols for "for all" and "there exist" may be okay in notes or homework, but are almost always written in words in more formal text.
    – babu_babu
    Dec 27, 2020 at 23:00

Same as for sine: "sine" in prose and "sin" in formulas. Of course, for formulas, you may be better served by "⇔". Depending on your intended audience, you may want to define whichever version you use before the first use.

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    In this case, I think it's more a matter of "sin" being another completely unrelated word. You wouldn't use "tan", "cot" or "sec" in prose either for similar reasons. The others ("cos", "csc") don't have that ambiguity issue, but are left with 3-letter abbreviations mostly for consistency I think. Dec 28, 2020 at 19:45

What type of physics text? A research paper? An introductory textbook? I'd say in general "iff" is fine to use in an educated setting iff material equivalence needs to be emphasized. Personally, I'd leave it out if not.

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