A century ago, Georg Cantor demonstrated the possibility of a series of
transfinite infinite numbers. His methods, unorthodox for the time,
enabled him to derive theorems that established a mathematical reality
for a hierarchy of infinities. Cantor's innovation was opposed, and
ignored, by the establishment; years later, the value of his work was
recognized and appreciated as a landmark in mathematical thought,
forming the beginning of set theory and the foundation for most of
contemporary mathematics.

As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure.

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As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure.

Download

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