Math Is Fun Forum

mamoo

Member

Registered: 2007-09-06

Posts: 3

Groups and neighbourhood

can someone explain to me groups and neighbourhood. i dont understand anything.
please help
thnx

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Groups and neighbourhood

I don't know either, but Wiki says neighborhood is a small disk-shaped space around a point where you can wiggle and still be in the set with that point or something.

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igloo myrtilles fourmis

dannyv

Member

Registered: 2007-09-20

Posts: 34

Re: Groups and neighbourhood

Group is simply a touple <A,*> where A is any set, and * is a binary operator with the following properties:
1) Asociative: for any a,b,c in A you have that (a*b)*c)=a*(b*c)
2) Neutral element: there is an element u in A where for any a in A you have that u*a=a
3) Opposite: for any element a in A there is another element called b such that b=-a

About the neighborhood I am not sure to what kind of neighbourhood you are referring to. For example in mathematical programming, a neighbourhood is simply a set of candidate solutions related to another candidate solution by means of a function called neighbourhood structure; this way defining the topology of the candidate solutions space, given an objective function.