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Sometimes I do read in a sentence:

some statement iff another statement

At first I thought it is a mispelling, but then I realized, that I do encounter this at many different posts. Does this mean equivalence?

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    Short answer: yes.2011-07-07
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    Slightly longer answer: yes. [Halmos claims to have invented it](http://en.wikipedia.org/wiki/Paul_Halmos) in his auto"math"ography *[I want to be a mathematician](http://books.google.com/books?id=F04PAQAAMAAJ)* as well as the qed-box $\blacksquare$ (more a big black upright rectangle it was, but I don't know the TeX-code for that).2011-07-07
  • 6
    Relevant: you can write the if-and-only-if symbol $\iff$ in $\LaTeX$ with `\iff`.2011-07-07
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    @Samuel: Good to know, thanks!2011-07-07
  • 0
    Just for interest $\phi$ 'just in case' $\theta$ is another way of saying $ \phi \iff \theta$2012-05-28
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    @PaulSlevin actually it is $\phi \Leftrightarrow \varphi$ and $\theta \Leftrightarrow \vartheta$.2012-07-12

3 Answers 3

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http://en.wikipedia.org/wiki/If_and_only_if using google helps a lot sometimes.

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    Generally you are right, but googling for **iff** alone is ambigious, see: [link][http://www.google.de/search?sourceid=chrome&ie=UTF-8&q=iff]. Ans since I am no native english speaker I didn't came up with **if and only if**. That's why I asked. And I am thankful for the short *and* the long answers. =)2011-07-07
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    @ Aufwind: For me the fourth link is http://en.wikipedia.org/wiki/IFF which directly leads you to the article i gave you :-) but no problem to ask.2011-07-07
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    Damn, I see that right now, too. *Fraunhofer* and *International Flowers* and the list of all the other *iff*s must have distracted me too much... No offense. :-)2011-07-07
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    @the responder: please do not discourage users to ask questions, while refering to google!2017-10-29
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As Zhen Lin already mentioned, "iff" is shorthand for "if and only if". Also in french literature one can find "ssi", which means "si et seulement si".

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    There is also a video by Serre, where he says he is thankful to the germans, who do not use "dannn" instead of "dann und nur dann".2011-07-07
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    I think it's in his lecture on *[How to write mathematis badly](http://www.dailymotion.com/video/xf88b5_jean-pierre-serre-writing-mathemati_tech)*, but I didn't have the patience to look for it in that video.2011-07-07
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    Thats exactly the one I meant.2011-07-07
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    J. H. Conway is always entertaining when he lectures. I recall that he got laughs when writing "unlesss" for "unless and only unless".2011-07-07
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    Jokes are easy. I once got a laugh from enlarging a model from $\mathfrak{A}$ to $\large{\mathfrak{A}}$.2011-07-07
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    Jokes are very useful. If the joke has a point, that point is likely to be remembered.2011-07-07
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    ssi is also used in Spanish (si y sólo si). I seem to recall I've also seen people write sii instead.2011-07-07
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    @Andres: as another spanish speaker (Argentina), i must say `ssi` in place of `si y sólo si` is not frequent in my experience.2011-07-07
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    @leonbloy: Yes, it figures. I remember its use as an undergrad, but don't know how frequent it is, I'm unfortunately very out of touch in this regard.2011-07-07
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    @Alexander: The Dutch write 'desda' for 'dan en slechts dan' - which points towards the more readable (and much more pronouncable!) 'dunda' for the Germans, the phrase means exactly the same.2011-07-07
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    @GEdgar: He seems like the kind of person who would also invent the words 'unlessss', 'unlesssss', ... - if that wasn't so pointless!2011-07-07
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    @yatima2975: we actually write "genau dann wenn" most of the time, which could be translated as "exactly if". It does not cause that repetitive sound you get when saying one of the other alternatives - which is probably why we don't have an abbreviation for it.2011-07-08
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    Well, I saw the abbreviation gdw for *genau dann wenn* quite a few times in lectures and talks. By the way: Serre makes his remark on "dannn" at 1:11 in [part III of the talk](http://www.dailymotion.com/video/xf88g3_jean-pierre-serre-writing-mathemati_tech). (The first minute is spent on iff and ssi)2011-07-08
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    Well yes, we have that abbreviation, but it does not have the form of a misspelling. :D2011-07-08
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Using your example:

some statement iff another statement.

This is a short-hand way of combining the "if-then" form of a statement, and its converse or the vice versa statement when they are both true:

  • if another statement, then some statement;

or

some statement, if another statement (1)


  • if some statement, then another statement;

or

another statement, if some statement (2)


Combining (1) and (2) gives:

some statement iff another statement.