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).

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.