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 8:07
The product of cardinals comes from the cartesian product.
|X| · |Y| = |X × Y|
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Anonymous2013-08-31 8:53
Infinity is often used not only to define a limit but as a value in the affinely extended real number system. Points labeled +\infty and -\infty can be added to the topological space of the real numbers, producing the two-point compactification of the real numbers.
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Anonymous2013-08-31 9:38
Cantor's work initially polarized the mathematicians of his day. While Karl Weierstrass and Dedekind supported Cantor, Leopold Kronecker, now seen as a founder of mathematical constructivism, did not.
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Anonymous2013-08-31 10:24
A large cardinal is a cardinal number with an extra property. Many such properties are studied, including inaccessible cardinals, measurable cardinals, and many more.
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Anonymous2013-08-31 11:09
This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition.