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 |
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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 |