difference
The difference of two numbers a and b is a number d such that
b+d=a. |
The difference of a (the minuend) and b (the subtrahend) is denoted by a-b.
The definition is for the elements a,b of any Abelian group (e.g. of a vector space
). The difference of them is always unique.
Note 1. Forming the difference of numbers (resp. elements), i.e. subtraction, is in a certain sense converse to the addition operation:
(x+y)-y=x |
Note 2. As for real numbers, one may say that the difference between a and b is |a-b| (which is the same as |b-a|); then it is always nonnegative. For all complex numbers, such a phrase would be nonsense.
Some
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•
b+(a-b)=a
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•
a-b=a+(-b)
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•
-(a-b)=b-a
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•
n(a-b)=na-nb (n∈ℤ)
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•
a-a= 0
Title | difference |
Canonical name | Difference |
Date of creation | 2013-03-22 17:33:35 |
Last modified on | 2013-03-22 17:33:35 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 16 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 20K99 |
Classification | msc 00A05 |
Classification | msc 11B25 |
Related topic | VectorDifference |
Related topic | SetDifference |
Related topic | Multiple |
Related topic | GeneralAssociativity |
Related topic | Quotient |
Related topic | DifferenceOfVectors |
Defines | minuend |
Defines | subtrahend |