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Definition-Theorem-Proof
David W. Lyons
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\(\DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\lcm}{lcm} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Perm}{Perm} \DeclareMathOperator{\Stab}{Stab} \DeclareMathOperator{\Orb}{Orb} \DeclareMathOperator{\Rot}{Rot} \DeclareMathOperator{\re}{Re} \DeclareMathOperator{\im}{Im} \DeclareMathOperator{\img}{image} \DeclareMathOperator{\conj}{conj} \DeclareMathOperator{\Id}{Id} \def\expi{E} \def\wrap{W} \newcommand{\C}{\mathbb{C}} \newcommand{\Quat}{\mathbb{H}} \newcommand{\extC}{\hat{\C}} \newcommand{\R}{\mathbb{R}} \newcommand{\extR}{\hat{\R}} \newcommand{\F}{\mathbb{F}} \newcommand{\extF}{\hat{\F}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Proj}{\mathbb{P}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\B}{\mathbb{B}} \newcommand{\M}{{\rm MOB}} \newcommand{\E}{{\rm EUC}} \renewcommand{\H}{{\rm HYP}} \newcommand{\HU}{\rm HYP_{\U}} \renewcommand{\S}{{\rm ELL}} \newcommand{\D}{\mathbb{D}} \newcommand{\closedD}{\hat{\D}} \newcommand{\U}{\mathbb{U}} \newcommand{\spacer}{\rule[0cm]{0cm}{0cm}} \newcommand{\MOD}{\mathbin{\text{MOD}}} \newcommand{\twotwo}[4]{\left[ \begin{array}{cc} #1 \amp #2 \\ #3 \amp #4 \end{array} \right]} \let\oldsection\section \renewcommand{\section}{\clearpage\oldsection} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Preface
0
Preliminaries
0.1
Basics of Sets and Functions
1
Logic
1.1
Boolean algebra
1.2
Equivalence of Logical and Boolean Expressions
1.3
Predicates and quantifiers
2
Sets
2.1
Characteristic Functions
3
Induction
3.1
Proof using mathematical induction
4
Relations
4.1
Basic objects
5
Functions
6
Elementary Number Theory
7
Cardinality
7.1
Shroeder-Bernstein Theorem
Back Matter
References
Definition-Theorem-Proof
David W. Lyons
Department of Mathematical Sciences
Lebanon Valley College
Annville, PA, USA
lyons@lvc.edu
©2025 David W. Lyons
January 2026 Edition, revised: December 26, 2025
Preface
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