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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“The contemporary thing in art and literature is the thing which doesn’t make enough difference to the people of that generation so that they can accept it or reject it.”
—Gertrude Stein (1874–1946)