Introduction to Mathematical Proofs: A Transition
Charles E. Roberts · 2009
Logic Statements, Negation, and Compound Statements Truth Tables and Logical Equivalences Conditional and Biconditional Statements Logical Arguments Open Statements and Quantifiers Deductive Mathematical Systems and Proofs Deductive Mathematical Systems Mathematical Proofs Set Theory Sets and Subsets Set Operations Additional Set Operations Generalized Set Union and Intersection Relations Relations The Order Relations , = Reflexive, Symmetric, Transitive, and Equivalence Relations Equivalence Relations, Equivalence Classes, and Partitions Functions Functions Onto Functions, One-to-One Functions, and One-to-One Correspondences Inverse of a Function Images and Inverse Images of Sets Mathematical Induction Mathematical Induction The Well-Ordering Principle and the Fundamental Theorem of Arithmetic Cardinalities of Sets Finite Sets Denumerable and Countable Sets Uncountable Sets Proofs from Real Analysis Sequences Limit Theorems for Sequences Monotone Sequences and Subsequences Cauchy Sequences Proofs from Group Theory Binary Operations and Algebraic Structures Groups Subgroups and Cyclic Groups Appendix: Reading and Writing Mathematical Proofs Answers to Selected Exercises References Index