n-ary Symmetric Difference
As above, the symmetric difference of a collection of sets contains just elements which are in an odd number of the sets in the collection:
- .
Evidently, this is well-defined only when each element of the union is contributed by a finite number of elements of .
Suppose is a multiset and . Then there is a formula for, the number of elements in, given solely in terms of intersections of elements of :
- ,
where is meant to indicate that is a subset of distinct elements of, of which there are .
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Famous quotes containing the word difference:
“One lesson we learn early, that in spite of seeming difference, men are all of one pattern. We readily assume this with our mates, and are disappointed and angry if we find that we are premature, and that their watches are slower than ours. In fact, the only sin which we never forgive in each other is difference of opinion.”
—Ralph Waldo Emerson (1803–1882)