Iff

Part of speech: conjunction

Definitions

1. A logical connective used in mathematics and logic to mean that two statements are true simultaneously if and only if both are true or both are false ; a shorthand symbol indicating a biconditional relationship between two propositions ; expressing equivalence such that one condition holds precisely when the other does
2. A symbol in formal logic denoting that two statements imply one another; representing a biconditional where each statement is necessary and sufficient for the other ; a notation used to show that both sides of an expression hold exactly under the same circumstances
3. An abbreviation used in logic to signify a biconditional statement where truth depends mutually on two propositions ; indicating that each of two expressions is both a necessary and sufficient condition for the other ; a concise representation specifying that the truth values of linked statements always correspond exactly

Etymology: "Iff" is a contraction of "if and only if," and its history is a neat piece of mathematical shorthand. The conjunction "if" descends from Old English "gif," and "and" and "only" are ordinary native English words, so nothing exotic lies in the parts. What is notable is the compression itself: the phrase became a single written abbreviation so that mathematicians could state biconditionals without repeating three words each time. The earliest well-attested use of the abbreviation appears in the mid-twentieth century, with the American mathematician John L. Kelley usually credited for popularising it in his 1955 textbook "General Topology." Logicians and mathematicians had written out the full phrase for centuries before that, and the contraction spread rapidly through mathematical writing because it was short enough to fit inline in proofs. Spoken aloud, "iff" is pronounced as a single syllable, and it is rarely heard outside mathematics and computer science, where precise definitions depend on it.

Synonyms: if and only if, equivalently