Chapter Zero Fundamental Notions of Abstract Mathematics

ISBN-10: 0201437244

ISBN-13: 9780201437249

Edition: 2nd 2001 (Revised)

Authors: Carol Schumacher

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Book details

List price: $117.80
Edition: 2nd
Copyright year: 2001
Publisher: Addison Wesley
Publication date: 11/17/2000
Binding: Paperback
Pages: 192
Size: 6.50" wide x 9.25" long x 0.50" tall
Weight: 1.232
Language: English

Introduction—an Essay
Mathematical Reasoning
Deciding What to Assume
What Is Needed to Do Mathematics? Chapter Zero
Logic
Statements and Predicates
Mathematical Implication
Direct Proofs
Compound Statements and Truth Tables
Equivalence
Proof by Contrapositive
Negating Statements
Proof by Contradiction
Existence and Uniqueness
Proving Theorems: What Now? Sets
Sets and Set Notation
Set Operations
Russell's Paradox
Relations and Ordering
Relations
Orderings
Equivalence Relations
Functions
Basic Ideas
Composition and Inverses
Order Isomorphisms
Sequences
Binary Operations
Induction
Inductive Reasoning and Mathematical Induction
Using Induction
Complete Induction
Elementary Number Theory
Natural Numbers and Integers
Divisibility in the Integers
The Euclidean Algorithm
Relatively Prime Integers
Prime Factorization
Congruence Modulo n
Divisibility Modulo n
Cardinality
Galileo's Paradox
Infinite Sets
Countable Sets
Beyond Countability
Comparing Cardinalities
The Continuum Hypothesis
Order Isomorphisms (Revisited)
The Real Numbers
Constructing the Axioms
Arithmetic
Order
The Least Upper Bound Axiom
Sequence Convergence in R
Axiomatic Set Theory
Elementary Axioms
The Axiom of Infinity
Axioms of Choice and Substitution
Constructing R
From N to Integers
From Integers to Rationals
From Rationals to R
Index
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