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

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.

Examples

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

  • if $p$ then $q$
  • if $q$ then $p$

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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