# Difference between revisions of "Iff"

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

− | In order to prove a statement of the form | + | In mathematical notation, "iff" is expressed as <math>\iff</math>. |

+ | |||

+ | 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]] | ||

{{stub}} | {{stub}} | ||

[[Category:Definition]] | [[Category:Definition]] |

## Latest revision as of 02:13, 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.

## Contents

## 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

*This article is a stub. Help us out by expanding it.*