presentations1

presentations1 - 18.100C Presentation topics for 9/10...

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

View Full Document Right Arrow Icon
18.100C Presentation topics for 9/10 Problem 1 (Rudin Problems 4,5 pg.22) Review the notion of upper and lower bound, infimum, and supremum, then solve: (i) Let E S be a nonempty subset of an ordered set S . Suppose α S is a lower bound of E and β S is an uppper bound of E . Prove that α β . (ii) Let A R be a nonempty subset of the real numbers. Define - A = {- x x A } to be the set of all numbers - x , where x A . Show that inf A = - sup( - A ). (Consider separately the cases when A is bounded below and when not.) Problem 2 (Rudin Problem 9 pg.22 – lexicographic order) Review the notion of ordered sets and least-upper-bound property, then solve: For complex numbers z = a + bi C and w = c + di C define “ z < w ” if either a < c or if ( a = c and b < d ). Prove that this turns C into an ordered set. Is this an ordered field? Does it have the least-upper-bound property? Problem 3
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/07/2011 for the course MATH 18.100B taught by Professor Prof.katrinwehrheim during the Fall '10 term at MIT.

Page1 / 2

presentations1 - 18.100C Presentation topics for 9/10...

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