1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
3 years ago
14

A and B are bounded non-empty subsets of R. For inf(A) to be less than or equal to inf(B), which of the following conditions mus

t be met?
a) For every b in B and epsilon > 0, there exists a in A, such that a < b + epsilon.

b) There exists a in A, and b in B such that a < b.

If neither of these conditions are appropriate, what would be appropriate conditions for inf(A) to be less than or equal to inf(B)?
Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

a) must be met

Step-by-step explanation:

We have two conditions:

a) For every b\in B and \epsilon>0, there exists a\in A, such that a.

b) There exists a\in A and b\in B such that  a.

We will prove that conditon a) is equivalent to inf(A)\leq inf(B)

If a) is not satisfied, then it would exist b\in B and \epsilon >0 such that, for every a\in A, a\geq b+\epsilon. This implies that b+\epsilon is a lower bound for A and in consequence

inf(A)\geq b+\epsilon > b\geq inf(B)

Then, inf(A) \leq inf(B) implies a).

If inf(A) \leq inf(B) is not satisfied then, inf(A) > inf(B) and in consequence exists b\inB such that b-inf(A)=\epsilon >0. Then b-\epsilon=inf(A) and, for every a\in A,

b-\epsilon =inf(A)\leq a.

So, a) is not satisfied.

In conclusion, a) is equivalent to inf(A)\leq inf(B)

Finally, observe that condition b) is not an appropiate condition to determine if inf(A)\leq inf(B) or not. For example:

  • <u>A={0}, B={1}</u>. b) is satisfied and inf(A)=0
  • <u>A={0}. B={-1,1}</u>. b) is satisfied and inf(A)=0>-1=inf(B)

You might be interested in
7. Ben's earnings for work he did from Monday through Saturday were: $78,
Agata [3.3K]

Answer:Average daily pay =$90

Step-by-step explanation:

Step 1

Formulae

Average daily earnings = Total amount of earning from Monday through Saturday/ number of days

Step 2

Monday   $78,

Tuesday   $94

Wednesday $115

Thursday     $108

Friday           $67

Saturday       $78

Total earnings for Ben = $540

Average daily pay= $540/6  ==$90

8 0
3 years ago
Aug 9, 2016 - ... a present she got for her little brother. How many square inches of giftwrap will beneeded to cover a box that
fenix001 [56]
It would be 48in because 4 times 6 is 24 and 24 times 2 is 48
5 0
3 years ago
Will this happen in avenger 4?
Marizza181 [45]

In chess, the Endgame is where you sacrafice pawns, or in this case, minor characters in order to get a powerful piece back. You can leave some pawns in battle while regaining power pieces. The pawns sacraficed were Peter, Stephen, Bucky, Drax, T'challa. Mantis, etc. While leaving behind two pawns: Nebula, and Bruce Banner. Normally I like to think of the Hulk as a Rook, but since he's completely useless at the moment, he's a pawn. Nebula's fairly worthless, so she's a pawn. Thanos is playing with all power pieces and one pawn: Gamora. He sacraficed his pawn in order to complete his queen equivilence: the gauntlet. Now he's playing with all power pieces, while the Avenger's have sacraficed their pawns in order to get their queen: Captain Marvel, who in turn will wage war on Thanos only to find that a pawn has made it across the board and turned into the Hulk, and fights side by side the original Avengers to get the soul stone, revive Tony, who probably dies, get their friends home, welcome new friends, and kill Thanos.

Sorry about the rambling. I'm not even sure if I got to the point.

4 0
3 years ago
Triangle PQR is transformed to similar triangle P′Q′R′ below:
morpeh [17]
1 over 3 should be the answer I think
6 0
3 years ago
5 1 point 34 is 68% of what number?​
Ilya [14]

Answer:

50

Step-by-step explanation:

Fastest method for calculating 34 is 68 percent of what number. Assume the unknown value is 'Y' 34 = 68% x Y. 34 = 68 / 100 x Y Multiplying both sides by 100 and dividing both sides of the equation by 68 we will arrive at: Y = 3 x 100 / 68. Y = 50%. Answer: 34 is 68 percent of 50

4 0
2 years ago
Other questions:
  • Find the Missing part of the unit rate: 40 students over 5 groups = ? Students over group
    9·1 answer
  • How is multiplying and dividing rational numbers similar<br> to multiplying and dividing integers?
    12·1 answer
  • Find the value of x.
    8·2 answers
  • What is the answer please im so anyyoned its inquatiltys and greater than less than please help
    5·1 answer
  • true or false the shortest distance from the center of the circumscribed circle to the sides of the inscribed triangle is the ci
    14·2 answers
  • Maryland's snowfall total for december was 1.43 inches and for January is was 12.67 inches
    13·1 answer
  • Evaluate the following expression 3xy; x = 4, y = -6
    14·2 answers
  • 5. What is ADCA?<br><br> A Acute<br> C Equiangular<br> D Not here<br> B Obtuse
    12·1 answer
  • Subtract right answers please
    14·2 answers
  • If you deposit $16,000 per year for 12 years (each deposit is made at the end of each year) in an account that pays an annual in
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!