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Cantor lived from 1845 to 1918, and worked out his theory of infinite sets from roughly 1870 to 1895. Cantor's verdict is that the set of even numbers, the set of odd numbers, the set of perfect squares, and the set of all the natural numbers have the same cardinality.
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www.earlham.edu/~peters/writing/infinity.htm
www.earlham.edu/~peters/writing/infinity.htm
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Survey from the Stanford Encyclopedia of Philosophy by Thomas Jec ... The fundamental concept in the theory of infinite sets is the cardinality of a set. ... What emerged is a hierarchy of properties of infinite sets, the Large Cardinal Theory, that appears to be the basis for the structure of the set theoretical universe.
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plato.stanford.edu/entries/set-theory/
plato.stanford.edu/entries/set-theory/
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the Theory of Infinite Sets ... In the years 1871-1884 Georg Cantor invented the theory of infinite sets. In the process Cantor constructed a set that is self-similar at all scales. Magnifying a portion of the set reveals a piece that looks like the entire set itself.
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www.exploratorium.edu/complexity/CompLexicon/settheory....
www.exploratorium.edu/complexity/CompLexicon/settheory.html
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Paradoxes of naive set theory (7 P) ... Pages in category "Basic concepts in infinite set theory" ... Dedekind-infinite set...
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en.wikipedia.org/wiki/Category:Basic_concepts_in_infini...
en.wikipedia.org/wiki/Category:Basic_concepts_in_infinite_set_theory
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Set theory - Wikipedia, the free encyclopedia
Set theory is the branch of mathematics 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 ...
en.wikipedia.org/wiki/Set_theory
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In the second half of the Nineteenth Century he and others worked out a theory of infinite sets which is outlined below. ... So far so good. Now what about infinite sets? Are there the same number of even whole numbers, as there are of all whole numbers -- or should there be only half as many even whole numbers?
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fclass.vaniercollege.qc.ca/web/mathematics/real/infinit...
fclass.vaniercollege.qc.ca/web/mathematics/real/infinity.htm
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We include Cantor in our historical overview, not because of his direct contribution to logic and the formalization of mathematics, but rather because he initiated the study of infinite sets and numbers which have provided such fascinating material, and difficulties, for logicians. ... Cantor's last two papers on set theory,
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www.math.uwaterloo.ca/~snburris/htdocs/scav/cantor/cant...
www.math.uwaterloo.ca/~snburris/htdocs/scav/cantor/cantor.html
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We in-vestigate three related questions: What kinds of infinite sets admit mechanical exhaustive search in finite time? How do we systematically build such sets? How fast can ... Our primary contribution is a comprehensive investiga-tion of such sets from the point of view of higher-type com-putability theory [18].
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www.cs.bham.ac.uk/~mhe/papers/exhaustive.pdf
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The history of set theory is rather different from the history of most other areas of mathematics. ... Bolzano defended the concept of an infinite set. At this time many believed that infinite sets could not exist. Bolzano gave examples to show that, unlike for finite sets, the elements of an infinite set could be put in 1...
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www.gap-system.org/~history/HistTopics/Beginnings_of_se...
www.gap-system.org/~history/HistTopics/Beginnings_of_set_theory.html
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