Definition:Iff

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Definition

The logical connective iff is a convenient shorthand for if and only if.


Notation

$A$ iff $B$ is generally symbolized by means of a two-headed arrow, for example:

$A \ \leftrightarrow \ B$
$A \ \Leftrightarrow \ B $
$A \ \longleftrightarrow \ B$
$A \iff B$


The notation used on $\mathsf{Pr} \infty \mathsf{fWiki}$ is $A \iff B$.


Also see


Internationalization

Iff is translated:

In Danish: hviss  (that is: hvis og kun hvis)
In Dutch: desda  (that is: dan en slechts dan als)
In Finnish: joss  (that is: jos ja vain jos)
In French: ssi  (that is: si et seulement si)
In German: gdw.  (that is: genau dann, wenn)
In Greek: ανν  (that is: αν και μόνο αν)
In Hebrew: אמ"ם  (that is: אִם וְרַק אִם)  Pronounced:  'eem v'rak 'eem
In Hindi: यकेय  (that is: यदि व केवल यदि)  Pronounced:  yadi va keval yadi
In Icelandic: eff  (that is: ef og aðeins ef)
In Polish: wtw  (that is: wtedy i tylko wtedy)
In Portuguese: sse  (that is: se e somente se)
In Spanish: ssi  (that is: si y sólo si)


Historical Note

The use of iff to mean if and only if is believed to have originated with Paul Halmos.


Sources