inverse number

The inverse number or reciprocal number of a non-zero 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 $a$).

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

• If $a$ ($\ne 0$) is given in a quotient form $\frac{b}{c}$, then its inverse number is simply

  $${\left(\frac{b}{c}\right)}^{-1}=\frac{c}{b}.$$

• 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 $ℝ$ resp. $ℂ$).

Title	inverse number
Canonical name	InverseNumber
Date of creation	2013-03-22 14:53:46
Last modified on	2013-03-22 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