## A First Course in Real Analysis |

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absolutely continuous Algebra Archimedean property Assuming bijective bounded function bounded sequence calculus called Cauchy's criterion chapter closed interval closed set completeness axiom conditions are equivalent continuous function convergent sequence Corollary decreasing Dedekind cut Definition deleted neighborhood endpoints example Exercise f(xn false explain field Q finite following conditions formula function F greatest lower bound Hint inequality irrational numbers largest element least upper bound Lebesgue-integrable Lemma Let F Let xn liminf limsup lower integrals metric space monotone negligible set nonempty set nonempty subset nonzero notations null sequence open intervals open set ordered field polynomial positive elements positive integer positive real number Proof Prove rational field rational number real number Riemann Riemann-integrable right continuous right differentiable right neighborhood sequence xn set of positive smallest element strictly increasing subdivision subinterval subsequence Suppose surjection True or false ultimately well-ordering property write