If and only if: Difference between revisions

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In logic and technical fields that depend on it, iff is used for "if and only if". It is often, not always, written italicized: iff. The abbreviation appeared in print for the first time in Kelley's 1955 book "General Topology" and was apparently invented by the mathematician Paul Halmos. The corresponding logical symbols are ↔ and ⇔.

A statement that is composed of two other statements joined by 'iff' is called a biconditional. Example of true statements that use "iff"--true biconditionals--are these:

That person is a bachelor iff that person is an unmarried man.

'Snow is white' (in English) is true iff 'schnee ist weiss' (in German) is true.

For any p, q, r: (p & q) & r iff p & (q & r). (Since this is written using variables and '&', the statement would usually be written using '↔', or one of the other symbols used to write biconditionals, in place of 'iff').

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-In [[mathematics]], [[logic]] and [[computer science]], '''iff''' is used for "if and only if". The corresponding logical symbols are &harr; and &hArr;.
+In [[logic]] and technical fields that depend on it, '''iff''' is used for "if and only if".  It is often, not always, written italicized: ''iff''.  The abbreviation appeared in print for the first time in Kelley's 1955 book "General Topology" and was apparently invented by the [[mathematician]] [[Paul Halmos]].  The corresponding logical symbols are &harr; and &hArr;.
+A statement that is composed of two other statements joined by 'iff' is called a [[biconditional]].  Example of true statements that use "iff"--true biconditionals--are these:
-The abbreviation appeared in print for the first time in Kelley's 1955 book "General Topology" and was apparently invented by the [[mathematician]] [[Paul Halmos]].
+:That person is a bachelor ''iff'' that person is an unmarried man.
+:'Snow is white' (in English) is true ''iff'' '<i>schnee ist weiss</i>' (in German) is true.
+:For any p, q, r: (p & q) & r iff p & (q & r).  (Since this is written using variables and '&', the statement would usually be written using '&harr;', or one of the other symbols used to write biconditionals, in place of 'iff').