Introduction to Proof in Abstract Mathematics
Courier Corporation, 10 de jun de 2014 - 384 páginas
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions.
Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.
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A E B arbitrary Assume Axiom Axiom of Choice bijection binary operation called cardinality Cauchy sequence codomain congruence contradiction Corollary coset countable deﬁne g Deﬁne the function deﬁning condition deﬁning property Deﬁnition Theorem denoted equivalence classes equivalence relation Example f is one-to-one ﬁrst ﬁxed formal deﬁnition function f given group G hypothesis induction Inference Rule inﬁnite isomorphism justiﬁcation language statements left inverse Let f Let G Let x e mathematics metalanguage n-set natural number need to show negation nonempty set normal subgroup notation one-to-one function order isomorphism poset proof of Theorem proof steps prop Prove Theorem real numbers right inverse rule for proving rules of inference Scrap Paper Section sequence subgroup of G Supplementary Problems Suppose symbol symmetry unique upper bound variable x e G