Please read up
https://groups.google.com/forum/#!topic/sci.math/8sY4Mcgkm1g
if it could help for databases.
This is a quick start:
Set U, e.g. R^2
Set U* set of all subsets of U including U and {}
Definitions:
A,B in U*
AnB {x:x in A and x in B} intersection
AuB {x:x in A or X in B} union
A\B {x:x in A and x not in B} without
Note that traditional set operations bind harder than definitions: (AuB)+(AnB). Further -negation binds hardest: -AuB=(-A)uB.
We are now defining algebraic compatible +/- operators:
A+B=AnB+AuB
A-B=A\B-B\A
A+{}=A
{}=-{}
Proof:
A-B=A+(-B)=An-B+Au-B=A\B-B\A
we choose AnB=A\B and AuB=-(B\A)
-A-B=-(A+B)=-Au-B+-An-B=-(AnB)-(AuB)
we choose -(AnB)=-Au-B and -(AuB)=-An-B
it holds:
-A\-B=B\A
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 113 |
Nodes: | 8 (1 / 7) |
Uptime: | 94:58:07 |
Calls: | 2,501 |
Calls today: | 2 |
Files: | 8,682 |
Messages: | 1,917,679 |