Analysis: An Introduction to Proof |
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a₁ accumulation point ANSWERS TO PRACTICE Archimedean property axiom of choice bijection cardinal number Cauchy sequence compact conclude continuous function converges uniformly Corollary countable definition denote denumerable derivative diverges equinumerous EXAMPLE Exercise Find finite formula function f ƒ and g ƒ is continuous ƒ is differentiable ƒ is integrable given implies induction inequality infinite injective interval of convergence Let f Let f(x Let ƒ lim inf lim sup m₁ mean value theorem N₁ natural numbers nonempty obtain open set ordered field ordered pairs P₁ partial sums partition polynomial positive number power series PRACTICE PROBLEMS Proof properties Prove that ƒ radius of convergence rational numbers real number Section series converges Show that ƒ statement subsequential limits subset Suppose that ƒ surjective Taylor's theorem true uniform convergence uniformly continuous upper bound