Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. please explain the solution and what it is wrong w

please explain the solution and what it is wrong with my conception. FOLLOW the COMMENT PLEASE Question: Let A...

60.1K

Verified Solution

Question

Advance Math

please explain the solution and whatit is wrong with my conception. FOLLOW theCOMMENT PLEASE

Question:

Let A and B are nonempty set bounded subset of R, and let A+B bethe set of all sums a+b where a belngs to A and b belongs to B

Prove Sup(A+B)=Sup(A)+Sup(B)

Solution: Let ε>0, a is in A and b is inB,

supA<=a+(ε/2), supB<=b+(ε/2)

sup(A + B) ≥ a + b ≥ sup A − ε /2 + sup B − ε /2 = sup A+ sup B − ε.

My Question:

1. Why the answer is not sup(A + B) ≥a+(ε/2)+b+(ε/2)=a+b+ε?

2. I don't understand why supA<=a+(ε/2),supB<=b+(ε/2)

is a+(ε/2) outside the upper bound or inside the lowerbound? why upperbound supA will less and equal to a+(ε/2). (pleasebetter draw the horizontal line and explain it)

Answer & Explanation Solved by verified expert
4.3 Ratings (648 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

A cone shaped container is oriented with its circular base on the top and its...

Geometry
Q

1.The yield of a one-year bond this year equals to 6.5%, and people expect the yield...

Finance
Q

The last assignment for this week is to submit by an attachment the product idea and/or...

Operations Management
Q

Use the following information regarding your retirement planning: You plan to work (and save) for 35 years,...

Finance
Q

Describe an operation where higher quality will cost more. What is your definition of quality? What...

General Management
Q

The following diagram shows two cell types a skin cell and an intestinal epithelial cell...

Biology
Q

Does the relation represent y as a function of x?2x=5y+3/(9y- 4)No because there are values...

Basic Math
Q

Computing Goodwill GoldStar Inc. acquired all assets and assumed all liabilities...

Accounting
Q

Brooklyn Studio's sales are all made on account. The firm's collection experience has been that...

Accounting
Q

Present Value of an Annuity of 1 Periods 8% 9% 10% 1 0.926 0.917 0.909...

Accounting
Q

all entries are for blue star airlineon May 1, 2022, Bluestar Airlines issues $500,000.04 percent...

Accounting
Q

Q1. Explain the difference between forward and backward looking marketing metrics. Give examples Q2.The newly...

Accounting