m090213 - Math 312, Intro. to Real Analysis: Midterm Exam...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 2

m090213 - Math 312, Intro. to Real Analysis: Midterm Exam...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online