If X and Y are disjoint, addition is given by the union of X and Y. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality, e.g., replace X by X×{0} and Y by Y×{1}.
|X| + |Y| = | X ∪ Y|.
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Anonymous2013-08-31 8:47
\int_{a}^{b} \, f(t)\ dt \ = \infty means that f(t) does not bound a finite area from a to b
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Anonymous2013-08-31 9:33
Set theory is the branch of mathematical logic that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.
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Anonymous2013-08-31 10:19
A recent area of research concerns Borel equivalence relations and more complicated definable equivalence relations. This has important applications to the study of invariants in many fields of mathematics.
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Anonymous2013-08-31 11:04
Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.