Difference between revisions of "Reciprocal"
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| − | The '''reciprocal''' of a non-[[zero]] number <math>r</math> (usually a [[real number]] or [[rational number]], but also a [[complex number]] or any non-zero element of a [[field]]) is its multiplicative [[inverse]]. The reciprocal is usually denoted <math>r^{-1}</math> or <math>\frac 1r</math>. | + | The '''reciprocal''' of a non-[[zero]] number <math>r</math> (usually a [[real number]] or [[rational number]], but also a [[complex number]] or any non-zero element of a [[field]]) is its multiplicative [[inverse with respect to an operation | inverse]]. The reciprocal is usually denoted <math>r^{-1}</math> or <math>\frac 1r</math>. |
<math>q</math> and <math>r</math> are multiplicative inverses of each other if and only if <math>r \times q = q \times r = 1</math>. | <math>q</math> and <math>r</math> are multiplicative inverses of each other if and only if <math>r \times q = q \times r = 1</math>. | ||
Revision as of 15:20, 15 August 2006
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The reciprocal of a non-zero number 
(usually a real number or rational number, but also a complex number or any non-zero element of a field) is its multiplicative inverse. The reciprocal is usually denoted 
or 
.
and are multiplicative inverses of each other if and only if 
.
