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:
“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has wished, drawing the sum of one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
—Friedrich Nietzsche (1844–1900)