An outline of set theory
This book is an innovative problem-oriented introduction to undergraduate set theory. It is intended to be used in a course in which the students work in groups on projects and present their solutions to the class. Students completing such a course come away with a deeper understanding of the material, as well as a clearer view of what it means to do mathematics. The topics covered include standard undergraduate set theory, as well as some material on nonstandard analysis, large cardinals, and Goodstein's Theorem. AN OUTLINE OF SET THOERY is organized into three parts: the first contains definitions and statements of problems, the second contains suggestions for their solution, and the third contains complete solutions.
What people are saying - Write a review
We haven't found any reviews in the usual places.
Part One Projects
Logic and Set Theory
32 other sections not shown
Other editions - View all
0Z z a a,fe a,ft adding numbers Axiom of Choice cardinal chapter commutative contradiction countable Dedekind finite definable subset Definition domain of g equivalence relation example false follows Godel's Goodstein's Theorem greatest element hence hyperreal infinite number infinite sets infinitesimal integers irreflexive least element least upper bound limit ordinal linear ordering mathematics maximal element N S(t natural numbers neg numbers Notation numbers is pos one-to-one function order-type Pair Set positive problem Project 28 proof of Theorem proper subset prove range of g rational numbers real numbers Regularity S(co S(ft schnitt sequence set by Comprehension set theory slot steps strongly inaccessible successor ordinal suggestions superbase Suppose Theorem 8.2 transfinite induction transitivity trichotomy true iff ultrafilter well-defined well-ordering Well-ordering Theorem write Zorn's Lemma