High Quality Content by WIKIPEDIA articles! In the mathematical
field of set theory, an ultrafilter on a set X is a collection of
subsets of X that is a filter, that cannot be enlarged (as a
filter). An ultrafilter may be considered as a finitely additive
measure. Then every subset of X is either considered "almost
everything" (has measure 1) or "almost nothing" (has measure 0). If
A is a subset of X, then either A or X A is an element of the
ultrafilter (here X A is the relative complement of A in X; that
is, the set of all elements of X that are not in A). The concept
can be generalized to Boolean algebras or even to general partial
orders, and has many applications in set theory, model theory, and
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