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Unformatted text preview: Math 312, Intro. to Real Analysis: Midterm Exam #1 Stephen G. Simpson Friday, February 13, 2009 1. True or False (3 points each) (a) Every ordered field has the Archimedean property. (b) The ordered field axioms imply | a- b | | a | + | b | for all a, b . (c) If lim a n =- then lim sup a n =- . (d) For any sequence of real numbers, the lim inf and the lim sup always exist and furthermore the lim inf is always the lim sup. (e) The equation 3 x 3 + 2 x 2 + 3 x + 2 = 0 has a rational solution. (f) 3 216 is an irrational number. (g) The limit of a convergent sequence of negative numbers is negative. (h) The limit of a convergent sequence of rational numbers is rational. (i) Every interval contains at least three rational numbers. (j) Every bounded sequence of real numbers is convergent. (k) Every convergent sequence of real numbers is bounded. (l) Every monotone sequence of real numbers is convergent....
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