Iff: Difference between revisions
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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. | 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: | 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>p</math> then <math>q</math> | ||
* if <math>q</math> then <math>p</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=== | ===Videos=== | ||
[https://www.youtube.com/embed/MckXBKafPfw Mathematical Logic] (I am in process of making a smoother version of this -themathematicianisin). | [https://www.youtube.com/embed/MckXBKafPfw Mathematical Logic] ("I am in process of making a smoother version of this" -themathematicianisin). | ||
==See Also== | ==See Also== | ||
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 
.
It is also known as a biconditional statement.
An iff statement 
means 
and 
at the same time.
Examples
In order to prove a statement of the form "
iff 
," it is necessary to prove two distinct implications:
- if
then 
- if then
Applications
Gödel's Incompleteness Theorem
Videos
Mathematical Logic ("I am in process of making a smoother version of this" -themathematicianisin).
See Also
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