Foundations of Higher MathematicsThis text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the students' ability to think mathematically and to distinguish mathematical thinking from wishful thinking. |
Contents
MATHEMATICAL INDUCTION | 59 |
68 | 85 |
COMBINATORIAL PROOFS | 95 |
Copyright | |
9 other sections not shown
Common terms and phrases
A₁ abelian Algebra Axiom of Choice belongs called cardinal number complex number consider contradiction countable set countably infinite Definition EXAMPLE denote directed graph disjoint divides divisor domain equivalence classes equivalence relation Figure finite set function f ƒ and g ƒ maps Give an example given greatest lower bound group G Hint homomorphism infinite set integer inverse isomorphic least member Lemma Let f Let ƒ Let G let h Mathematical Induction modulo multiplication natural number nonempty set notation one-to-one function one-to-one function mapping operation ordered pairs partial order partition permutations positive integers positive real number Principle of Mathematical PROOF Let PROOF See Exercise Prove Proposition Prove Theorem Prove your answer r₁ rational numbers real number reflexive Schroeder-Bernstein Theorem set theory subgroup of G symmetric transitive true uncountable set X₁