# Does “iff” mean “if and only if” $(\Longleftrightarrow)$?

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. – Zhen Lin Jul 7 '11 at 12:10
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
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

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 iffs 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
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
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
ssi is also used in Spanish (si y sólo si). I seem to recall I've also seen people write sii instead. – Andrés E. Caicedo Jul 7 '11 at 17:01

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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