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Logic and Proof for Teachers
Lesa L. Beverly, Kimberly M. Childs, Thomas W. Judson, Deborah A. Pace
Contents
Index
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Contents
Prev
Up
Next
Front Matter
Colophon
Preface
Contributors to the 2019 Edition
1
Logic
Definitions
Compound Statements
Tautologies, Contradictions, & Quantifiers
Propositional Functions and Quantifiers
2
Arguments and Proofs
Deductive Reasoning
Three Forms of Valid Arguments
Proofs
3
Sets
Sets
4
Relations
Relations
Equivalence Relations
Functions and Cardinality
5
Integers and the Division Algorithm
Mathematical Induction
The Division Algorithm
Prime Numbers
Back Matter
A
More on the Integers
Strong Induction
The Connection between Mathematical Induction and the Principle of Well Ordering
The Proof of the Fundamental Theorem of Arithmetic
B
Notation
C
GNU Free Documentation License
Index
Colophon
Authored in PreTeXt
π
Chapter
5
Integers and the Division Algorithm
ΒΆ
π
The integers are the building blocks of mathematics. In this chapter we will investigate the fundamental properties of the integers, including mathematical induction, the division algorithm, and the Fundamental Theorem of Arithmetic.
5.1
Mathematical Induction
5.2
The Division Algorithm
5.3
Prime Numbers
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