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I've come across a lot of posts where "iff" is used as a short form for "if, and only if,". Maybe it's just me, but when trying to read (a long text) fast, I think it's easy to misunderstand it for just "if". Another problem I find is that non-English speakers may have it tougher to realize what it means. They may have not read too much mathematics in English and assume it's just a typo for "if"

I understand this is a widely spread convention, but this does not make it right. I am also aware that the use of abbreviations if often discouraged in most Stack Exchange communities, but I am not sure of how that applies here. Has this (or a similar) concern being expressed before? Should "iff" be accepted or discouraged?

NOTE: Please don't take this as a request for "action". I am not asking for "iff" to be banned from use or anything similar. I am just trying to gather community opinion/advice about its convenience.

ANOTHER NOTE: Some people who read this post have failed to understand that the main problem I have with "iff" is that it is easy to mistake for "if" when reading (even when you are aware of "iff"'s existence!), not that it is an abbreviation, nor that people may not be used to it. Please be smart and don't be one of those

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    $\begingroup$ I don't think this particular abbreviation is something worthwhile taking action on. I do think we should discourage excessive use of abbreviations and encourage clarification of lesser recognized abbreviations. To give a slightly more extreme comparison, I would also not agree to discourage "etc." in favor of "et cetera". It's also probably unenforceable, and I'm not a big fan of unenforceable prohibitions, as long as what they prohibit isn't that big of a deal. $\endgroup$ – rschwieb Jul 10 at 13:27
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    $\begingroup$ @rschwieb You are probably right that no action should be taken. But "not wanting to ban something" something is not the same as "thinking something is awesome". The "etc." case seems to me like a bad example, sinsce there is no other similar word that "etc." could be mistaken with $\endgroup$ – David Jul 10 at 13:32
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    $\begingroup$ Should we discourage the use of confusing acronyms? (E.g., "i.e." is often used to mean "e.g.", i.e. "i.e." is used incorrectly, and we wouldn't want that.) $\endgroup$ – Asaf Karagila Jul 10 at 13:41
  • $\begingroup$ You're right, the analogy isn't perfect. I just wanted an example of a well-established abbreviation and its full form not being worth taking action about. $\endgroup$ – rschwieb Jul 10 at 13:42
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    $\begingroup$ @rschwieb: That would have been a fantastic opportunity to refer to some links (cf. this and that post), and you've missed it. $\endgroup$ – Asaf Karagila Jul 10 at 13:43
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    $\begingroup$ @rschwieb Of course! But the point I'm making is not "please avoid iff because it's an abbreviation" but rather "please avoid iff because it can be confused in a way that drastically changes the meaning of the statement". Confusing "i.e." with "e.g." implies very little information lost $\endgroup$ – David Jul 10 at 13:44
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    $\begingroup$ You're right, the difference in meaning is of a greater magnitude. Maybe your concern can evolve into a refinement of the advice on posting. You could possibly add advice to this which says something like "review your answer for abbreviations and terminology which may trip up unfamiliar readers, and consider replacing it with clearer terms or otherwise explaining." $\endgroup$ – rschwieb Jul 10 at 13:48
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    $\begingroup$ The abbreviation "iff" is universally used. It appears in papers and mathematical literature without comments. If you do not like it, do not use it yourself (I find myself using it less and less each day, and I think a reasonable argument can be made in this regard, along lines very different from the ones in the post). Nothing else ought to be done. $\endgroup$ – Andrés E. Caicedo Jul 10 at 19:47
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    $\begingroup$ I don't understand the negative feedback. Even if you don't agree with my assumptions, why isn't this an legitimate question? $\endgroup$ – David Jul 11 at 8:30
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    $\begingroup$ Nobody said it's not a legitimate question. Voting on meta is about agreement with the content. You suggest to discourage "iff", and people disagree with that. $\endgroup$ – Asaf Karagila Jul 11 at 8:32
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    $\begingroup$ @AsafKaragila Then why is this quesiton on hold? $\endgroup$ – David Jul 12 at 7:01
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    $\begingroup$ I don't know. My guess? You're insisting that you're misunderstood, you're calling people stupid, and meta is for discussions. If you just disagree with everything people tell you, and if you skip the discussion to use the "iff" example in the FAQ answer you wrote, then people figure that this is not an honest question and vote to close. That's just my take on this, ultimately you'd have to ask those who voted, and they are not obligated to answer. $\endgroup$ – Asaf Karagila Jul 12 at 7:13
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    $\begingroup$ The abbreviation "iff" is indeed standard, and I learned it within the first few weeks of university. I never once saw it in high school, so I think it is worth expanding it when explaining something high school-level. $\endgroup$ – Theo Bendit Jul 18 at 3:08
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    $\begingroup$ I've seen John Conway use "onne" for "one and only one", "twwo" for "two and only two", .... $\endgroup$ – Gerry Myerson Jul 24 at 22:25
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    $\begingroup$ @David, if I've told you once, I've told you a thousand times: don't exaggerate! $\endgroup$ – Gerry Myerson Aug 1 at 10:15
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I don't think this should be discouraged any more than the use of $\mathbf{R}$ to denote the set of real numbers.1

The use of "iff" is quite common through mathematics. In my second or third week we were given a homework assignment for the first time with an "iff" (or its Hebrew equivalent אםם, which makes even less syntactical sense, since ם is a letter that only appears at the end of a word, and there it was in the middle).2

Our TA explained that this is not a typo, but rather a common shorthand in mathematics. It took a bit to get used to it. But at the end of the day, this is part of standard mathematics.

There's no reason to discourage this use or edit it out. It can be your choice to not use it, and I understand and even appreciate this choice (I don't I've used this all that much outside $\iff$, maybe on rare occasions). But this is something so standard that policing it would be ridiculous. The most I can offer you is to lead by example.


  1. Of course the real numbers should be denoted by $\omega^\omega$, but $\Bbb R$ is the appropriate font if one chooses a boldfaced version. Any claim otherwise is by definition a mistake.

  2. The word "אם" is the Hebrew word for "if", so in that sense אםם is a very good translation of "iff".

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    $\begingroup$ I think this answer still misses the main point that "If" and "iff" are hard to distinguish at first glance. But what could possible be mistaken for $\mathbb{R}$ $\endgroup$ – David Jul 10 at 13:52
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    $\begingroup$ Mathematics is, ultimately, an art of attention to details. (Possible conflict of interest: this user is not always very attentive to details.) $\endgroup$ – Asaf Karagila Jul 10 at 13:54
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    $\begingroup$ Ok, I will define my six variables as $X_{x_x}, x_x, \chi_x, \kappa_\chi, x_\chi$ and expect you to correctly identify each of them correctly $\endgroup$ – David Jul 10 at 14:01
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    $\begingroup$ And I will use four different P's in different typefaces to mean different things. Also, let $\Xi$ be a complex number, and consider $$\frac{\Xi}{\overline{\Xi}}$$ $\endgroup$ – Asaf Karagila Jul 10 at 14:03
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    $\begingroup$ (Also, I have to cringe every time people use $\omega$ and especially $\omega_n$ for anything other than the ordinals. Yes, math is full of symbol overloading. What's your point? That we need to read carefully and pay attention? That's my point too!) $\endgroup$ – Asaf Karagila Jul 10 at 14:06
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    $\begingroup$ Yes, we should be careful when reading math. But the author should also be careful in making that task as easy as possible for that by using clear, easily identifiable language and notation. I don't think that's a revolutionary idea $\endgroup$ – David Jul 10 at 14:11
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    $\begingroup$ I don't think so either. But it's a common abbreviation, and it isn't going anywhere. So it's not a revolutionary idea either to help people get used to it by exposing them to it more often. $\endgroup$ – Asaf Karagila Jul 10 at 14:20
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    $\begingroup$ Well, I strongly disagree with that. I don't think you should annoying language and notation in your writings in order to make people familiar with nuisance. Instead, I try to write "properly" (what I consider "proper writing" at least) in order to make people see how easier like is if we all do so! $\endgroup$ – David Jul 10 at 14:22
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    $\begingroup$ Well. We start with "iff", then with "LEM" and "ZFC" and "NBG" or "KM". Next comes "AC/DC" and then "IVT, MVT, FLT" and so on. Abbreviations are part of the lingo. That is a fact that you might as well get used to, here and elsewhere in life. Yes, we shouldn't rely on them too much, but when they are common enough, then context should be enough. And yes, I agree we should be clear for newcomers, non-native speakers, and others. But we should also provide the ladder to encourage people to use Google, to search, to investigate, and teach themselves new things. $\endgroup$ – Asaf Karagila Jul 10 at 14:25
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    $\begingroup$ And at the end of the day, if someone doesn't know what "iff" stands for, there's always the comments section to ask for clarification on that. And doing it once should be enough for a lifetime per person. $\endgroup$ – Asaf Karagila Jul 10 at 14:25
  • $\begingroup$ $$\mathbb{R}_+,\mathbb{R}_-,\mathbb{R}^2$$ just to list a few... as for identifying symbols deterify, and TeX command option in show math. $\endgroup$ – Roddy MacPhee Jul 11 at 1:26
  • $\begingroup$ I think @Roddy meant "detexify". $\endgroup$ – Gerry Myerson Jul 24 at 22:24
  • $\begingroup$ @Gerry probably because I don't use it. $\endgroup$ – Roddy MacPhee Jul 24 at 22:55
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Remark: Right in the begin I would like to emphasize that I do understand what you want to discuss: the problem of misinterpreting "iff" as "if" while reading through a post, here on MSE.

That to be said I would like to add that I am in fact a non-native English speaker. Yes, it was confusing in the first place to encounter "iff" and yes, hence it was not in a paper if I remember correctly, I thought it would be a typo. Nevertheless, I looked it up and since then I never had to do so again (as Asaf Karagila said "doing it once should be enough for a lifetime per person").
Arguing in your way one should als rethink the heavy usage of "i.e." as it could be mistaken for "is" as I have seen it only written as "ie". Or the one of "a.e." which could be mistaken for "as". And I bet you can find more and more examples if you think long enough.

So, the problem might not uniquely occure in the case of "iff" but for other, commonly used abbreviations too. Moreover, as it was already pointed out several times, "iff" is also quite common used in professional papers so why "ban" it to be used here on MSE (I know, you do not want to ban the usage completely but rather know how the community thinks about this issue; but this point was thrown in not only once...).

For myself I appreciate the usage of "iif", "w.l.o.g.", "a.e", etc. pp. as it helps me, again from the point of view of a non-native speaker, to actually learn those common abbreviations. Sure, I have to look them up; but normally only once to keep it. As MSE is a forum designed to learn mathematics why not learn the language used within mathematics too?

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    $\begingroup$ Arguably, wlog can be mistaken as a typo for $\log$. And E.g. could be mistaken for $E_g$. $\endgroup$ – Asaf Karagila Jul 15 at 10:42
  • $\begingroup$ @AsafKaragila I agree. That is why I decided to write "And I bet you can find more and more examples (as you did) if you think long enough" to point out that "iff" is not the only case where some kind of misinterpretation can happen. $\endgroup$ – mrtaurho Jul 15 at 10:44

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