Difference between revisions of "Involution"
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== Properties == | == Properties == | ||
* An function is an involution [[iff]] it is symmetric about the line <math>f(x)=x</math> in the coordinate plane. | * An function is an involution [[iff]] it is symmetric about the line <math>f(x)=x</math> in the coordinate plane. | ||
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Revision as of 18:48, 27 September 2008
An involution is a function whose inverse is itself.
Examples
- The function
has the inverse 
, which is the same function, and thus 
is an involution. - The logical NOT is an involution because $\neg \neg p} \equiv p$ (Error compiling LaTeX. Unknown error_msg).
- The additive negation is an involution because
. - The multiplicative inverse is an involution because
. In fact, for any 
, 
is an involution.
has the inverse 
, which is the same function, and thus 
is an involution.
.
. In fact, for any 
, 
is an involution.Properties
- An function is an involution iff it is symmetric about the line in the coordinate plane.
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