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Hey!

Name: Dick 2009-11-29 21:28

Stop grabbing me!

Name: Anonymous 2009-11-29 21:29

never

Name: Anonymous 2009-11-29 21:29

*grabs dick*

Name: Anonymous 2009-11-29 21:58

never

Name: !HOXIp0gGW6 2009-11-29 21:59

*grabs Dickie*

Name: HAXUS THE SAGE 2009-11-30 8:49

HAXUS THE SAGE

Name: Anonymous 2011-02-04 18:37

Name: Anonymous 2011-02-04 19:27

Name: Anonymous 2013-08-31 22:49


The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874–1884. Cardinality can be used to compare an aspect of finite sets; e.g. the sets {1,2,3} and {4,5,6} are not equal, but have the same cardinality, namely three (this is established by the existence of a one-to-one correspondence between the two sets; e.g. {1->4, 2->5, 3->6}).

Name: Anonymous 2013-08-31 23:34


Using König's theorem, one can prove κ < κcf(κ) and κ < cf(2κ) for any infinite cardinal κ, where cf(κ) is the cofinality of κ.

Name: Anonymous 2013-09-01 0:19


The formula would be useful neither to compute the force between two objects of finite mass nor to compute their motions. If an infinite mass object were to exist, any object of finite mass would be attracted with infinite force (and hence acceleration) by the infinite mass object, which is not what we can observe in reality.

Name: Anonymous 2013-09-01 1:05


The most widely studied systems of axiomatic set theory imply that all sets form a cumulative hierarchy. Such systems come in two flavors, those whose ontology consists of:

Name: Anonymous 2013-09-01 1:51


One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers. This method is used, for example, in the proof that there is no free complete lattice.

Name: Anonymous 2013-09-01 2:35


The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are well-ordered: every nonempty subset of the natural numbers has a unique least element under the natural ordering.

Name: Anonymous 2013-09-01 3:21


Examples of category-theoretic statements which require choice include:
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