Question

Show that a bounded decreasing sequence converges to its greatest lower bound.

Show that a bounded decreasing sequence converges to its greatest lower bound.

Homework Answers

Answer #1

Using the concept of bounded decreasing sequence I solve the problem .

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
If a bounded sequence is the sum of a monotone increasing and a monotone decreasing sequence...
If a bounded sequence is the sum of a monotone increasing and a monotone decreasing sequence (xn = yn + zn where {yn} is monotone increasing and { zn} is monotone decreasing) does it follow that the sequence converges? What if {yn} and {zn} are bounded?
Show that every nonempty subset of the real numbers with a lower bound has a greatest...
Show that every nonempty subset of the real numbers with a lower bound has a greatest lower bound.
Show that if sequence (an) converges, then all the rearrangement of (an) converges, and converge to...
Show that if sequence (an) converges, then all the rearrangement of (an) converges, and converge to the same limit
Determine whether the sequence is increasing, decreasing, or monotonic. Is the sequence bounded? an= 9n +...
Determine whether the sequence is increasing, decreasing, or monotonic. Is the sequence bounded? an= 9n + 1/n
Suppose (an) is an increasing sequence of real numbers. Show, if (an) has a bounded subsequence,...
Suppose (an) is an increasing sequence of real numbers. Show, if (an) has a bounded subsequence, then (an) converges; and (an) diverges to infinity if and only if (an) has an unbounded subsequence.
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and...
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and equals inf{an}.
Find the least upper bound and the greatest lower bound for the two polynomials: a) p(x)...
Find the least upper bound and the greatest lower bound for the two polynomials: a) p(x) = x4 - 3x2 - 2x + 5 b) p(x) = -2x5 + 5x4 + x3 - 3x + 4
Suppose (an), a sequence in a metric space X, converges to L ∈ X. Show, if...
Suppose (an), a sequence in a metric space X, converges to L ∈ X. Show, if σ : N → N is one-one, then the sequence (bn = aσ(n))n also converges to L.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
Show that sequence {sn} converges if it is monotone and has a convergent subsequence.
show that a sequence of measurable functions (fn) converges in measure if and only if every...
show that a sequence of measurable functions (fn) converges in measure if and only if every subsequence of (fn) has subsequence that converges in measure
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT