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If and only if (i.e., Necessary and Sufficient). The terms ``Just If'' or ``Exactly When'' are sometimes used instead. $A$ iff $B$ is written symbolically as $A\leftrightarrow B$. $A$ iff $B$ is also equivalent to $A\Rightarrow B$, together with $B\Rightarrow A$, where the symbol $\Rightarrow $ denotes ``Implies.''

J. H. Conway believes that the word originated with P. Halmos and was transmitted through Kelley (1975). Halmos has stated, ``To the best of my knowledge, I DID invent the silly thing, but I wouldn't swear to it in a court of law. So there--give me credit for it anyway'' (Asimov 1997).

See also Equivalent, Exactly One, Implies, Necessary, Sufficient


Asimov, D. ``Iff.'' posting, Sept. 19, 1997.

Kelley, J. L. General Topology. New York: Springer-Verlag, 1975.

© 1996-9 Eric W. Weisstein