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<->B, A<=>B, A<->B, or A <==> B. A iff B is also equivalent to A=>B together with B=>A, where the symbol => denotes "implies." Other equivalent terms are "A is equivalent to B" (A=B) and "A XNOR B."

J. H. Conway believes that the word originated with P. Halmos and was transmitted through Kelley (1955, p. 232), where it is stated "F is equicontinuous at x iff there is a neighborhood of x whose image under every image of F is small."

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" (D. Asimov, pers. comm., Sept. 19, 1997).

See also

At Least One, Equivalent, Exactly One, Implies, Necessary, Sufficient, XNOR

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Asimov, D. "Iff." posting, Sept. 19, 1997.Kelley, J. L. General Topology. New York: Springer-Verlag, 1955.Simpson, J. A. and Weiner, E. S. C. (Preparers). The Compact Oxford English Dictionary, 2nd ed. Oxford, England: Clarendon Press, p. 812 (Band 7, p. 636), 1992.

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Cite this as:

Weisstein, Eric W. "Iff." From MathWorld--A Wolfram Web Resource.

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