inverse number
The inverse number or reciprocal number of a nonzero real or complex number^{} $a$ may be denoted by ${a}^{1}$, and it the quotient^{} $\frac{1}{a}$ (so, it is really the ${1}^{\mathrm{th}}$ power of $a$).

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Two numbers are inverse numbers of each other if and only if their product is equal to 1 (cf. opposite inverses^{}).

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If $a$ ($\ne 0$) is given in a quotient form $\frac{b}{c}$, then its inverse number is simply
$${\left(\frac{b}{c}\right)}^{1}=\frac{c}{b}.$$ 
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Forming the inverse number is also a multiplicative function, i.e.
$${(bc)}^{1}={b}^{1}{c}^{1}$$ (to be more precise, it is an automorphism^{} of the multiplicative group^{} of $\mathbb{R}$ resp. $\u2102$).
Title  inverse number 
Canonical name  InverseNumber 
Date of creation  20130322 14:53:46 
Last modified on  20130322 14:53:46 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  12 
Author  pahio (2872) 
Entry type  Definition 
Classification  msc 12E99 
Classification  msc 00A05 
Synonym  inverse 
Synonym  reciprocal 
Related topic  ConditionOfOrthogonality 
Related topic  InverseFormingInProportionToGroupOperation 
Defines  reciprocal number 