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."
If and only if proofs often contain two parts. The first is the "if" part, which is reletively straightforward. The second is the "only if" part. To prove this, you need to show that the to prove is only satisfied by the given. This is typically more difficult than the "if" part.
 
  
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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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