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Author: Robert Roth Stoll. 133 downloads 1934 Views 21MB Size Report. This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site.
A book of set theory / Charles C Pinter. p. cm. “A revised and corrected republication of Set Theory, originally published in 1971 by Addison-Wesley Publishing Company, Reading, Massachusetts.” Summary: “This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each
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BABY SET THEORY We shall begin with an informal discussion of some basic concepts of set theory. In these days of the "new math," much of this material will be already familiar to you. Indeed, the practice of beginning each mathematics course with a discussion of set theory has become widespread, extending even to the elementary schools.
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- Sets
- Topological Spaces
- Proposition 9.
set is a collection of objects, called its elements. We write x 2 A to mean that x is an element of a set A, we also say that x belongs to A or that x is in If A and B are sets, we say that B is a subset of A if every element of B is an element of A. In this case we also say that A. Two sets are considered equal i A B and B A. contains B, and we wr...
Let X be a set. A topology on X is a collection of subsets of X, ie,
Let (X; d) be a metric space. Then X is Hausdor ogy. with the metric topol- Let (X; <) be a totally ordered set. Then X is Hausdor topology. with the order
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Basic Set Theory. A set is a Many that allows itself to be thought of as a One. - Georg Cantor This chapter introduces set theory, mathematical in- duction, and formalizes the notion of mathematical functions. The material is mostly elementary. For those of you new to abstract mathematics elementary does not mean simple (though much of the ...
4.7 Embedding mathematics into set theory 4.7.1 Z 4.7.2 Q 4.7.3 R 4.8 Exercises 5. In nite numbers 62 5.1 Cardinality 5.2 Cardinality with choice 5.3 Ordinal arithmetic 5.4 Cardinal arithmetic 5.5 Co nality 5.6 In nite operations and more exponentiation 5.7 Counting 5.8 Exercises 6. Two models of set theory 85 6.1 A set model for ZFC 6.2 The ...
