Question: Let 0 SCR be bounded above and u R. Prove that the following two conditions are equivalent: 1. u = sup S. 2. For

Let 0 SCR be bounded above and u R. Prove that the

Let 0 SCR be bounded above and u R. Prove that the following two conditions are equivalent: 1. u = sup S. 2. For every > 0 we have (a) u + is an upper bound for S, and (b) u-e is NOT an upper bound for S. - State and prove the analogue of the previous exercise for inf S.

Step by Step Solution

★★★★★

3.36 Rating (146 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

A machine used for lling plastic bottles with a soft drink has a known standard deviation of = 0.05 liter. The target mean ll volume is = 2.0 liters. (a) Describe the sampling distribution of x,...

Prove that the following functions are cdfs. (a) +4tan-1 (z),ZE (-00,00) (c) e- , z (-o, 00) (e) the function defined in (1.5.6) (1+e-*)-I,ZE (-00,00) (b) (e) (b) (d) z E (-o0, oo) 1-e-z,-e (0,00)

Prove that the following is similarity invariant: Rank

Prove that the following formulas define norms on R2: (a) ||v|| = 221 + 3v22 (b) ||v|| = 2v21] - v1v2 + 2v22 (c) ||v|| =2|v1| + |v2| (d) ||v|| = max{ 2|v1|, |v2| } (e) ||v|| = max{ |v1, - v2|, |v1 +...

Jackson is a manager who is preparing to send a memo to members of his team. What will best help him evaluate the memo before sending it? Multiple Choice surveying team members consulting the Ethics...

MAT1325 : Homework #2 Prof : Monica Nevins Due Thursday, February 4, 2016 by 9pm at the Department of Mathematics and Statistics (KED) Staplers are not available at the Department. Instructions : sh...

Hi, I am in difficulty when I kept trying to do these questions. Could you give me a help to solve these questions? Thank you so much. Note: I attach the extra information as well Q1 (7 points) 4-l-1...

1. Extreme points of polytopes with a lower bound on the number of positive components. Let X = {x E R" : Aa = b, c > 0} be a polytope, where A is an m x n matrix of rank m. equivalent (a) Prove that...

Need help with question 5, see question 3 for lexicographic preference relation as instructed in question 5. 3. Let X be a set. and let :1 and :3 be two binary relations on X. Define the...

As the picture shows. 1. Extreme points of polytopes with a lower bound on the number of positive components. Let X = {:13 E R\" : Ax = 12,21: 2 0} be a polytope, where A is an m x n matrix of rank...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

What are the primary characteristics of residential mortgage loans? Why does the ratio of adjustable-rate mortgages to fixed-rate mortgages in the economy vary over an interest rate cycle? When would...

What are some examples of conceptual aspects of the user interface?

Select all that apply. what is the most effective way to determine if your guests have drank prior to arrival

Identify each of the following accounts of Advanced Services Co. as asset, liability, stock-holders equity, revenue, or expense, and state in each case whether the normal balance is a debit or a...

Roth AG has a deferred tax liability of 68,000 at the beginning of 2022. At the end of 2022, it reports accounts receivable on the books at 90,000 and the tax basis at zero (its only temporary...

Why is the von Neumann bottleneck important?

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suitsclubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9,...

In any process the maximum amount of heat that can be converted to mechanical energy a. depends on the amount of friction present b. depends on the intake and exhaust temperatures c. depends on...

An ad for ADT Security Systems says, "When you go on vacation, burglars go to work [...] According to FBI statistics, over 25% of home burglaries occur between Memorial Day to Labor Day." Question 1...

Let f : (0, ) R be differentiable on (0, 1) and assume that f(x) b as x 1. (b) Show that if f(x) a as x , then b = 0. lim (f(x + h)-))ib. lim (f(x)/x) b

Prove that n3 + (n + 1)3 + (n + 2)3 is divisible by 9 for all n N.

Let I := [a, b and let f : I R be a continuous function such that f(x) > 0 for each x in I. Prove that there exists a number a > 0 such that f(x) > a for all x I.

Express the following ratios in its lowest terms. 0. 84 : 1.4 : 1.96

Solve the following proportions for the unknown quantities 625:f:500 = g:3:4

Solve the following proportions for the unknown quantities 6:7:5 = n:105:m