Question: Let (an) nEN be a sequence such that lim inf an = 0. Prove there is a subsequence (any ) KEN such that _=] ank

Let (an) nEN be a sequence such that lim inf an

= 0. Prove there is a subsequence (any ) KEN such that

Let (an) nEN be a sequence such that lim inf an = 0. Prove there is a subsequence (any ) KEN such that _=] ank converges

Step by Step Solution

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 Mathematics Questions!

Q:

James and Esther Johnson live at 45678 S.W. 112th Street, Homestead, FL 33033. James, who is 67 years old (date of birth 12/14/1949), is retired receiving social security benefits, and Esther, who is...

Q:

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

Q:

1 Let (an) nen be a sequence. (a) Prove that if lim an = L exists, then every subsequence of (an)ner tends to L. 1-+0o (b) Prove that if every subsequence of (an )nel is convergent, then (an)EN is...

Q:

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...

Q:

MAT 137Y: Calculus! Problem Set 7. Due in tutorial on July 27/28 Instructions: Print this cover page, fill it out entirely, sign at the bottom, and STAPLE it to the front of your problem set (You do...

Q:

A) Let {xn } be a bounded sequence. Prove directly using the denition of lim inf and lim sup that there exists two possibly dierent subsequences {xnk } and {xnk } of {xn } where lim inf xk = lim xnk...

Q:

Let (an) be a fixed, bounded sequence. For each n N+, set Sn = = sup{an, an+1, an+2,...} and tn = inf{an, an+1, an+2,...}. Also, set s = inf{sn: n N+} and t := sup{tn : n N+}. This s is called the...

Q:

10. Show that linear combinations of sequences that converge in measure on a set of finite measure also converge in measure. Please use following theories to prove (no need to use all of them, 1 or 2...

Q:

a) Let (s n ) (0, +) be a sequence of real numbers. Prove that lim inf (1/s n ) = 1 / (lim sup s n ) b) Let (a n ) (0, 100) be a sequence of real numbers, assuming that there are two subsequences (n...

Q:

Use Theorem 21.18 for a new proof of Lvy's continuity theorem (Problem 21.3 ). (i) Show (as in Problem 21.3 ) that \(\lim _{i ightarrow \infty} \int u d \mu_{i}\) exists for all \(u \in...

Q:

A random experiment consists of throwing two three-sided dice (showing the numbers 1, 2, 3). Let X be the random variable which records the average of the pair of numbers showing on the dice. (i)...

Q:

Consider 100.0 g samples of two different compounds consisting only of carbon and oxygen. One compound contains 27.2 g of carbon, and the other has 42.9 g of carbon. How can these data support the...

Q:

Step 7 Now we must find the time ( in s ) at which the mass attains its extreme displacement from the equilibrium position. This is the instant at which the mass ceases to move away from the...

Q:

A. Calculate the value of (T 2 -T 1 ) where T 1 is the initial temperature and T 2 is the final temperature. Express your answer numerically. View Available B. Part complete Calculate the value of...

Q:

There has been much discussion in the news lately over the effect of false news websites on the election results. See for example:...

Q:

QUESTION 1 Calculate the spindle speed in RPM of a lathe turning a 96 millimeter diameter material that requires a cutting speed of 148 SMPM. QUESTION 2 Calculate the feed rate in inches per minute...

Q:

how does budget help organizations make good decision?

Q:

Is it possible to achieve an enterprise vision with a decentralized IT function?

Q:

Create a 200 word summary on the Juvenile Justice System than and today. Describe The Juvenile system and provide a generalizable definition. Highlight the issues in the Juvenile system and why this...

Q:

Intermediate An investment project has the following expected cash flows over its economic life of three years: Required: (i) Calculate the net present value (NPV) of the project at discount rates of...

Q:

Intermediate: Calculation of payback, NPV and ARR for mutually exclusive projects Your company is considering investing in its own transport fleet. The present position is that carriage is contracted...

Q:

Intermediate: NPV and payback calculations You are employed as the assistant accountant in your company and you are currently working on an appraisal of a project to purchase a new machine. The...