Combinatorial Sum
The restriction of unions to disjoint unions is an important one; however, in the formal specification of symbolic combinatorics, it is too much trouble to keep track of which sets are disjoint. Instead, we make use of a construction that guarantees there is no intersection (be careful, however; this affects the semantics of the operation as well). In defining the combinatorial sum of two sets and, we mark members of each set with a distinct marker, for example for members of and for members of . The combinatorial sum is then:
This is the operation that formally corresponds to addition.
Read more about this topic: Symbolic Combinatorics
Famous quotes containing the word sum:
“I would sum up my fear about the future in one word: boring. And that’s my one fear: that everything has happened; nothing exciting or new or interesting is ever going to happen again ... the future is just going to be a vast, conforming suburb of the soul.”
—J.G. (James Graham)