Art of Problem Solving

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The '''reciprocal''' of a non-[[0|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 \cdot q = q \cdot r = 1</math>.
 
== See Also ==


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>.
*[[Operator inverse]]


<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>.
[[Category:Definition]]
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Latest revision as of 10:25, 15 February 2025

The reciprocal of a non-zero number $r$ (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 $r^{-1}$ or $\frac 1r$.

$q$ and $r$ are multiplicative inverses of each other if and only if $r \cdot q = q \cdot r = 1$.

See Also

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