Introduction to the Theory of Sets
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.
Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to its grasp, declares author Joseph Breuer, is patience. Breuer illustrates the grounding of finite sets in arithmetic, permutations, and combinations, which provides the terminology and symbolism for further study. Discussions of general theory lead to a study of ordered sets, concluding with a look at the paradoxes of set theory and the nature of formalism and intuitionalism. Answers to exercises incorporated throughout the text appear at the end, along with an appendix featuring glossaries and other helpful information.
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LibraryThing ReviewUser Review - jamessavik - LibraryThing
This book is a reasonable, if unspectacular, introduction to set theory and set operations. It is suitable for undergraduate level mathematics. Read full review
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accumulation point algebraic numbers belong Bolzano-Weierstrass theorem bounded called Cantor chemistry closed interval complementary set concept continuous functions continuum contradiction covering set deﬁned deﬁnition dense-in-itself denumerable set empty set equivalence theorem equivalent sets example Exercises Figure ﬁnite cardinal numbers ﬁnite number ﬁnite sets ﬁrst element ﬁrst point formalists fractions greater cardinal number Hence inﬁnite number inﬁnite sets integral introduction intuitionalism intuitionalists lattice points laws line segment linear mapping mathematical natural numbers neighboring points number of elements numbers is denumerable one-to-one correspondence ordered set ordinal ordinal-type paradoxes placed in one-to-one point set points interior prime numbers problems proof proper subset prove quantum mechanics rational numbers rational points real numbers relation sequence set of lattice set of numbers set of points set of real set theory sets are equivalent signiﬁcance similar straight line theory of sets transcendental numbers transﬁnite cardinal numbers well-ordered set well-ordering theorem