division (original) (raw)

The quotient (or ratio) ab of a and b may be defined as such a number (or element of the field) x that b⋅x=a. Thus,

which is the “fundamental property of quotient”.

The quotient of the numbers a and b (≠0) is a uniquely determined number, since if one had

then we could write

from which the supposition b≠0 would imply x-y=0, i.e.x=y.

Title division
Canonical name Division
Date of creation 2014-08-08 17:51:29
Last modified on 2014-08-08 17:51:29
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 29
Author pahio (2872)
Entry type Definition
Classification msc 00A05
Classification msc 12E99
Related topic InverseFormingInProportionToGroupOperation
Related topic DivisionInGroup
Related topic ConjugationMnemonic
Related topic Difference2
Related topic UniquenessOfDivisionAlgorithmInEuclideanDomain
Defines quotient
Defines ratio
Defines fundamental property of quotient
Defines reduction