Suppose that E, A, B R and E = A U B. Prove that if E

Question:

Suppose that E, A, B ⊂ R and E = A U B. Prove that if E has a supremum and both A and B are nonempty, then sup A and sup B both exist, and sup E is one of the numbers sup A or sup B.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 03:53 AM

See More Questions

Suppose that E is a compact subset of X. a) If f, g : E Rn are uniformly continuous, prove that f + g and f g are uniformly continuous. Did you need compactness for both results? b) If g: E R is...
a) Suppose that E is a two-dimensional region and that S = {(x, y, z) R3: (x, y) E and z = 0}. Prove that and that for each continuous g : E R. b) Let f : [a, b] R be a Cp function, let C be the...
Suppose that, for each of three age groups (25-34, 35-44, and 45-54), we have recorded yearly sex-specific lung cancer mortality rates for the five-year period 19! through 1994. These data are to be...
Craps is a dice game in which two fair dice are cast. If the roller shoots a 7 or 11 on the rst roll, he or she wins. If the roller shoots a 2, 3, or 12 on the rst roll, he or she loses. (a) Compute...
The trustee in the bankruptcy settlement for Titanic Boat Co. lists the following book values and liquidation values for the assets of the corporation. Liabilities and stockholders claims are shown....
Prepare a frequency distribution for each data set in Problems 24-27. Consider the following data sets: Data set D Data set A: The annual wages of employees at a small accounting firm are given in...
For each of the following situations, calculate the $t$-statistic $(t)$ : a. $\mathrm{X}^{-}=11.00 ; \mu=5 ; s \mathrm{X}^{-}=3.00$ b. $X^{-}=26.00 ; \mu=31 ; s X^{-}=2.00$ c. \(X^{-}=19.60 ;...
Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 19-51. If each internal resistance is r = 0.100 , and R = 4.00, what is the voltage across the resistor...
A standardization battle is underway in the market for electric cars, with BMW, Nissan, Tesla and Toyota investing to establish their technology as the dominant standard. In the battle, Tesla has...
Replace the force and couple system by an equivalent force and couple moment at point O. Units Used: kN = 103 N Given: M = 8kNm = 60 deg a = 3 m f = 12 b = 3 m g = 5 c = 4 m F1 = 6kN d = 4m F2 = 4kN...
a) Prove that if x is an upper bound of a set E R and x E, then x is the supremum of E. b) Make and prove an analogous statement for the infimum of E. c) Show by example that the converse of each...
A dyadic rational is a number of the form k/2n for some k, n Z. Prove that if a and b are real numbers and a < b, then there exists a dyadic rational q such that a < q < b.
Ratios are an important part of financial analysis. Divide into groups of two or three. Each person should choose one year from the Home Depot 2015 Annual Report in Appendix A. Calculate the current...
International Reporting Case Walgreens (USA) is the leading drug store chain in the United States. The company provided the following disclosures related to its retirement benefits in its 2013 annual...
Listed below are SAT scores from a sample of students (based on data from www.talk.collegeconfidential.com). Why is it that a graph of these data will not be very effective in helping us understand...
Graph the returns for residential and commercial on a time series. Does there appear to exist a lead/lag relationship? If so, by how many months? Is the relationship statistically significant?
Graph the residential and commercial year-over-year time series. Does residential lead commercial? By how many months? Is the relationship statistically significant?
Portillo Inc. uses a calendar year for financial reporting. The company is authorized to issue 9,000,000 R$10 par ordinary shares. At no time has Portillo issued any potentially dilutive securities....
The following terms were introduced in this chapter: 1. Profit and loss ratio 2. Admission by investment 3. Partnership liquidation 4. Mutual agency 5. Salary allowance 6. Withdrawal by payment from...
Identify the most stable compound:
Perform the same computation as Sec. 24.1, but compute the amount of heat requited to raise the temperature of 1200 g of the material from -150 to 100C. Use Simpsons rule for your computation, with...
Repeat Prob. 24.1, but use Romberg integration to s = 0.0 1%.
Repeat Prob. 24.1, but use a two- and a three-point Gauss Legendre formula. Interpret your results.
Problem: Module 3 Textbook Problem 5 Learning Objective: 3-6 Using the straight-line method show how bonds issued at a discount. affect financial statements Diaz Company issued $91,000 face value of...
Manvir had to make payments of $1,125 every 6 months to settle a $22,000 loan that he received at 4.52% compounded semi-annually. a. How long did it take to settle the loan?
If I invest a single amount of $14,000 in an account earning 8% p.a. compounding quarterly for 5 years, how much interest will I have earned in those 5 years?

Suppose that E, A, B R and E = A U B. Prove that if E

Question:

Step by Step Answer:

Since A E any upper bound of E is an upper bound of A Since A is nonempty it follows from ...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions