Question

let A be a nonempty subset of R that is bounded below. Prove that inf A...

let A be a nonempty subset of R that is bounded below. Prove that inf A = -sup{-a: a in A}

Homework Answers

Answer #1

i hope you like it... this is very famous question of real analysis.. thanks dear

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose A ⊆ R is nonempty and bounded above and β ∈ R. Let A +...
Suppose A ⊆ R is nonempty and bounded above and β ∈ R. Let A + β = {a + β : a ∈ A} Prove that A + β has a supremum and sup(A + β) = sup(A) + β.
Let A⊆R be a nonempty set, which is bounded above. Let B={a-5:a∈ A}. Prove that sup(B)=sup(A)-5
Let A⊆R be a nonempty set, which is bounded above. Let B={a-5:a∈ A}. Prove that sup(B)=sup(A)-5
Let S and T be nonempty subsets of R with the following property: s ≤ t...
Let S and T be nonempty subsets of R with the following property: s ≤ t for all s ∈ S and t ∈ T. (a) Show that S is bounded above and T is bounded below. (b) Prove supS ≤ inf T . (c) Given an example of such sets S and T where S ∩ T is nonempty. (d) Give an example of sets S and T where supS = infT and S ∩T is the empty set....
Prove that if E ⊂ R is bounded and sup E ∈ E or inf E...
Prove that if E ⊂ R is bounded and sup E ∈ E or inf E ∈ E, then E is not open. Analysis question (R refers to the real numbers).
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤...
Question 3. Let a1,...,an ∈R. Prove that (a1 + a2 + ... + an)2 /n ≤ (a1)2 + (a2)2 + ... + (an)2. Question 5. Let S ⊆R and T ⊆R be non-empty. Suppose that s ≤ t for all s ∈ S and t ∈ T. Prove that sup(S) ≤ inf(T). Question 6. Let S ⊆ R and T ⊆ R. Suppose that S is bounded above and T is bounded below. Let U = {t−s|t ∈ T, s...
Let f : [a,b] → R be a bounded function and let:             M = sup...
Let f : [a,b] → R be a bounded function and let:             M = sup f(x)             m = inf f(x)             M* =sup |f(x)|             m* =inf |f(x)| assuming you are taking values of x that lie in [a,b]. Is it true that M* - m* ≤ M - m ? If it is true, prove it. If it is false, find a counter example.
Prove: A nonempty subset C⊆R is closed if and only if there is a continuous function...
Prove: A nonempty subset C⊆R is closed if and only if there is a continuous function g:R→R such that C=g-1(0).
Let A be open and nonempty and f : A → R. Prove that f is...
Let A be open and nonempty and f : A → R. Prove that f is continuous at a if and only if f is both upper and lower semicontinuous at a.
1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove...
1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove that if u and v are both least upper bounds of S, then u = v. (b) Let a > 0 be a real number. Define S := {1 − a n : n ∈ N}. Prove that if epsilon > 0, then there is an element x ∈ S such that x > 1−epsilon.
Suppose S and T are nonempty sets of real numbers such that for each x ∈...
Suppose S and T are nonempty sets of real numbers such that for each x ∈ s and y ∈ T we have x<y. a) Prove that sup S and int T exist b) Let M = sup S and N= inf T. Prove that M<=N
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT