More General Usage
Iff is used outside the field of logic, wherever logic is applied, especially in mathematical discussions. It has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon. (However, as noted above, if, rather than iff, is more often used in statements of definition.)
The elements of X are all and only the elements of Y is used to mean: "for any z in the domain of discourse, z is in X if and only if z is in Y."
Read more about this topic: If And Only If
Famous quotes containing the words general and/or usage:
“We ought, says Kant, to become acquainted with the instrument, before we undertake the work for which it is to be employed; for if the instrument be insufficient, all our trouble will be spent in vain. The plausibility of this suggestion has won for it general assent and admiration.... But the examination can be only carried out by an act of knowledge. To examine this so-called instrument is the same as to know it.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“I am using it [the word ‘perceive’] here in such a way that to say of an object that it is perceived does not entail saying that it exists in any sense at all. And this is a perfectly correct and familiar usage of the word.”
—A.J. (Alfred Jules)