The difference of two numbers a and b is a number d such that


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 groupMathworldPlanetmath (e.g. of a vector spaceMathworldPlanetmath). 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:


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 numbersMathworldPlanetmathPlanetmath, such a phrase would be nonsense.


  • b+(a-b)=a

  • a-b=a+(-b)

  • -(a-b)=b-a

  • n(a-b)=na-nb(n)

  • 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 QuotientPlanetmathPlanetmath
Related topic DifferenceOfVectors
Defines minuend
Defines subtrahend