opposite number

The opposite number of a number a is such a number  -a  that

-a+a= 0.

Some properties:

  • -a=(-1)a

  • -0= 0

  • -(-a)=a

  • -(a+b)=(-a)+(-b)

  • -(ab)=a(-b)=(-a)b

  • -(a-b)=b-a

  • -j=1naj=j=1n(-aj)

  • -abf(x)𝑑x=baf(x)𝑑x

Exactly similar properties (except the last) are valid in every ring.  The fifth property implies the

Corollary.  If one changes the sign of one factor of a ring product, then the sign of the whole product changes.

Title opposite number
Canonical name OppositeNumber
Date of creation 2013-03-22 15:03:25
Last modified on 2013-03-22 15:03:25
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Definition
Classification msc 97D99
Classification msc 12D99
Synonym negative [as a noun]
Related topic Ring
Related topic OppositePolynomial
Related topic ConditionOfOrthogonality
Related topic Automorphism4
Related topic ProductOfNegativeNumbers
Related topic PlusSign