Does "iff" mean "if and only if" $(\Longleftrightarrow)$?

Question

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?

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 07 '11 at 12:14
Relevant: you can write the if-and-only-if symbol $\iff$ in $\LaTeX$ with \iff. — Samuel, Jul 07 '11 at 15:07
Just for interest $\phi$ 'just in case' $\theta$ is another way of saying $ \phi \iff \theta$ — Paul Slevin, May 28 '12 at 23:22
@PaulSlevin actually it is $\phi \Leftrightarrow \varphi$ and $\theta \Leftrightarrow \vartheta$. — haunted85, Jul 12 '12 at 23:10

score 10 · Accepted Answer · answered Jul 07 '11 at 12:13

10

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

answered Jul 07 '11 at 12:13

Listing

13,937

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. =) – Aufwind Jul 07 '11 at 12:41
@ 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. – Listing Jul 07 '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 07 '11 at 12:47
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@the responder: please do not discourage users to ask questions, while refering to google! – user1511417 Oct 29 '17 at 21:11

score 4 · Answer 2 · answered Jul 12 '12 at 22:17

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.

score 4 · Answer 3 · answered Jul 07 '11 at 12:14

4

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".

answered Jul 07 '11 at 12:14

Alexander Thumm

5,112

6

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 07 '11 at 12:19
2

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 07 '11 at 12:26
Thats exactly the one I meant. – Alexander Thumm Jul 07 '11 at 12:31
5

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 07 '11 at 14:48
Jokes are easy. I once got a laugh from enlarging a model from $\mathfrak{A}$ to $\large{\mathfrak{A}}$. – Jay Jul 07 '11 at 15:02
Jokes are very useful. If the joke has a point, that point is likely to be remembered. – André Nicolas Jul 07 '11 at 15:09
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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. – Andrés E. Caicedo Jul 07 '11 at 17:01
@Andres: as another spanish speaker (Argentina), i must say ssi in place of si y sólo si is not frequent in my experience. – leonbloy Jul 07 '11 at 17:47
@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. – Andrés E. Caicedo Jul 07 '11 at 18:15
@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. – yatima2975 Jul 07 '11 at 20:02
@GEdgar: He seems like the kind of person who would also invent the words 'unlessss', 'unlesssss', ... - if that wasn't so pointless! – yatima2975 Jul 07 '11 at 20:13
@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. – Alexander Thumm Jul 08 '11 at 07:26
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. (The first minute is spent on iff and ssi) – t.b. Jul 08 '11 at 09:31
Well yes, we have that abbreviation, but it does not have the form of a misspelling. :D – Alexander Thumm Jul 08 '11 at 09:36

Does "iff" mean "if and only if" $(\Longleftrightarrow)$?

3 Answers3