[CSUSB] >> [CNS] >> [Comp Sci Dept] >> [R J Botting] >> [MATHS] >> intro_note
[Index] || [Contents] || [Source] || [Definitions] || [Search] || [Notation] || [Copyright] || [Comment] Fri Jan 16 12:31:59 PST 2004

Note

A><B::=Set of Pairs, first element in A and second in B, is an informal definition of the Cartesian product of A and B. The following is a formal definition as a type of object that has a documented structure with two components labelled 1st and 2nd:
A><B::= $ Net{1st:A, 2nd:B}. Now 1st and 2nd in the above act like be mappings or functions from A><B into A and B respectively:
1st:A><B ->A,
2nd: A><B -> B. Further maps can be described as special relations:
A->B::={R:Relations(A,B)| for all a:B, one b:B(a R b)} Now relations are described as special sets of pairs
For Types T1,T2, A:@T1, B:@T2, Relations(A,B)::=@(T1><T2).
...which is where we came in.
What is important at the start is to learn how all the different notations fit together, not which notation is actually defined in terms of which other notation. The 'best' way to do this is a meta-mathematical problem.