Download presentation

Presentation is loading. Please wait.

Published byDulcie Richardson Modified over 2 years ago

1
MAT 3749 Introduction to Analysis Section 1.1 The Real Numbers http://myhome.spu.edu/lauw

2
Math Party?

3
Actuarial Presnentation Cambia/Regence 10/17 3pm OMH 126

4
Preview Field, Ordered Field Lower/Upper Bounds Supremum/ Infimum

5
References Section 1.1 Howland, Section 1.5

6
Introduction: A Story… You are in a foreign country and want to buy….

7
Before going into that,.. We will briefly mention the field properties and that the real numbers R is a field.

8
Before going into that,.. We will briefly mention the field properties and that the real numbers R is a field.

9
Field

10
Real Numbers R The set R of Real Numbers is a field.

11
Example 1 (a) Q is a field. (b) Z is not a field. (Why?)

12
Ordered Field

13
Real Numbers R The set R of Real Numbers is an ordered field.

14
Example 2 C is a field but not an ordered field.

15
Move On… More properties of R. First important milestone of an analysis class – supremum / infimum (Allow us to prove results such as Intermediate Value Theorem)

16
Upper (Lower) Bounds Similar for bounded below, lower bound, and minimum element

17
Example 3 1. Determine which of the following sets are bounded above. 2. Determine which of the following sets have a maximum element.

18
Example 3 (a) AnalysisSolution

19
Example 3 (b) AnalysisSolution

20
Example 3 (c) AnalysisSolution

21
Archimedean Property

22
Density Property

23
Least Upper Bounds Similar for greatest lower bound, and infimum

24
Equivalent Statement Similar for greatest lower bound, and infimum

25
Example 4 Show that AnalysisSolution

26
Example 5 Determine the supremum of AnalysisSolution

27
The Completeness Axiom

Similar presentations

OK

Introduction to Real Analysis Dr. Weihu Hong Clayton State University 8/19/2008.

Introduction to Real Analysis Dr. Weihu Hong Clayton State University 8/19/2008.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on file system in unix file Maths ppt on real numbers class 10 Ppt on social networking good or bad Ppt on kindness is contagious Ppt on mobile tv Ppt on power sharing in democracy people Ppt on company profile of hdfc bank Elements of one act play ppt on tv Ppt on shell scripting interview Ppt on ms project 2010