If and only if (i.e., necessary and sufficient). The terms "just if" or "exactly when" are sometimes used instead.
iff 
is written symbolically as 
, 
,
, or 
. 
iff 
is also equivalent to 
together with 
,
where the symbol 
denotes "implies." Other equivalent terms are
"
is equivalent
to 
" (
) and "
XNOR 
."
J. H. Conway believes that the word originated with P. Halmos and was transmitted through Kelley (1955, p. 232), where it is stated "
is equicontinuous at 
iff there is a neighborhood of 
whose image under every image of 
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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References
Asimov, D. "Iff." math-fun@cs.arizona.edu 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 Resource. https://mathworld.wolfram.com/Iff.html