If and Only If - More General Usage

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:

    “The general public is easy. You don’t have to answer to anyone; and as long as you follow the rules of your profession, you needn’t worry about the consequences. But the problem with the powerful and rich is that when they are sick, they really want their doctors to cure them.”
    —Molière [Jean Baptiste Poquelin] (1622–1673)

    “Pythagoras, Locke, Socrates—but pages
    Might be filled up, as vainly as before,
    With the sad usage of all sorts of sages,
    Who in his life-time, each was deemed a bore!
    The loftiest minds outrun their tardy ages.”
    —George Gordon Noel Byron (1788–1824)