PlanetMath: inverse number

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inverse number

(Definition)

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

Two numbers are inverse numbers of each other if and only if their product is equal to 1 (cf. opposite inverses).
If ( $\neq 0$ ) is given in a quotient form $\frac{b}{c}$ , then its inverse number is simply
$\displaystyle \left(\frac{b}{c}\right)^{-1} = \frac{c}{b}.$
Forming the inverse number is also a multiplicative function, i.e.
$\displaystyle (bc)^{-1} = b^{-1}c^{-1}$
(to be more precise, it is an automorphism of the multiplicative group of $\mathbb{R}$ resp. $\mathbb{C}$ ).

"inverse number" is owned by pahio.

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Other names:

inverse, reciprocal

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Cross-references: multiplicative group, automorphism, multiplicative function, opposite inverses, product, power, quotient, complex number, real
There are 74 references to this entry.

This is version 8 of inverse number, born on 2004-12-14, modified 2007-01-14.
Object id is 6578, canonical name is InverseNumber.
Accessed 8599 times total.

Classification:

AMS MSC:	00A05 (General :: General and miscellaneous specific topics :: General mathematics)
	12E99 (Field theory and polynomials :: General field theory :: Miscellaneous)

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