Analysis: with an introduction to proof
By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs.Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises.A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.
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accumulation point ANSWERS TO PRACTICE Archimedean property axiom of choice bijective cardinal number Cauchy sequence closed sets conclude continuous function contradiction convergent sequence converges uniformly Corollary countable DEFINITION Let denote denumerable derivative differentiable diverges elements equinumerous equivalence class equivalence relation EXAMPLE Let EXERCISES Exercises marked exists a number exists a point Figure function defined give a counterexample given hints or solutions implies injective Justify each answer Key Terms later sections Let f(x lim sup Mark each statement mathematical induction mean value theorem metric space natural numbers nonempty subset open cover open set ordered field ordered pairs partition positive number power series properties Prove or give Prove the following rational numbers real number Review of Key sections and exercises series converges statement True subsequential limits Suppose surjective Terms in Section THEOREM Let triangle inequality True or False uniformly continuous