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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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3  
Short answer: yes. –  Zhen Lin Jul 7 '11 at 12:10
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Slightly longer answer: yes. Halmos claims to have invented it in his auto"math"ography I want to be a mathematician 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). –  t.b. Jul 7 '11 at 12:14
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Relevant: you can write the if-and-only-if symbol $\iff$ in $\LaTeX$ with \iff. –  Samuel Jul 7 '11 at 15:07
    
@Samuel: Good to know, thanks! –  Aufwind Jul 7 '11 at 15:09
    
Just for interest $\phi$ 'just in case' $\theta$ is another way of saying $ \phi \iff \theta$ –  Paul Slevin May 28 '12 at 23:22

3 Answers 3

up vote 10 down vote accepted

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][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. =) –  Aufwind Jul 7 '11 at 12:41
    
@ Aufwind: For me the fourth link is en.wikipedia.org/wiki/IFF which directly leads you to the article i gave you :-) but no problem to ask. –  Listing Jul 7 '11 at 12:43
    
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. :-) –  Aufwind Jul 7 '11 at 12:47

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". –  Alexander Thumm Jul 7 '11 at 12:19
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I think it's in his lecture on How to write mathematis badly, but I didn't have the patience to look for it in that video. –  t.b. Jul 7 '11 at 12:26
    
Thats exactly the one I meant. –  Alexander Thumm Jul 7 '11 at 12:31
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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". –  GEdgar Jul 7 '11 at 14:48
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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. –  Andres Caicedo Jul 7 '11 at 17:01

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.

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