Difference between revisions of "Iff"

Latest revision as of 01:13, 24 December 2020

Iff is an abbreviation for the phrase "if and only if."

In mathematical notation, "iff" is expressed as $\iff$ .

It is also known as a biconditional statement.

An iff statement $p\iff q$ means $p\implies q$ and $q\implies p$ at the same time.

In order to prove a statement of the form " $p$ iff $q$ ," it is necessary to prove two distinct implications:

Mathematical Logic ("I am in process of making a smoother version of this" -themathematicianisin).

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 '''Iff''' is an abbreviation for the phrase "if and only if."
-In order to prove a statement of the form, "A iff B," it is necessary to prove two distinct implications: that A implies B ("if A then B") and that B implies A ("if B then A").
+In mathematical notation, "iff" is expressed as <math>\iff</math>.
-If a statement is an "iff" statement, then it is a [[biconditional]] statement.
+It is also known as a [[conditional|biconditional]] statement.
+An iff statement <math>p\iff q</math> means <math>p\implies q</math> <b>and</b> <math>q\implies p</math> at the same time.
+==Examples==
+In order to prove a statement of the form "<math>p</math> iff <math>q</math>," it is necessary to prove two distinct implications:
+* if <math>p</math> then <math>q</math>
+* if <math>q</math> then <math>p</math>
+===Applications===
+[https://artofproblemsolving.com/wiki/index.php/Godel%27s_First_Incompleteness_Theorem Gödel's Incompleteness Theorem]
+===Videos===
+[https://www.youtube.com/embed/MckXBKafPfw Mathematical Logic] ("I am in process of making a smoother version of this" -themathematicianisin).
 ==See Also==
+* [[Logic]]
-[[logic]]
+{{stub}}
 [[Category:Definition]]
-{{stub}}