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).
