# Proving a Set E is Compact

Not what you're looking for?

Please see the attached file for the fully formatted problems.

Let lambda n be a real decreasing sequence converging to

Prove E is compact if and only if = 0.

I am assuming compactness here refers to the sequential compactness. This

seems to make the most sense. Since this problem is an analysis problem,

please be sure to be rigorous, and include as much detail as possible so that

I can understand. Please also state if you are making use of some fact or

theorem. Thanks!

##### Purchase this Solution

##### Solution Summary

A set E is proven to be sequentially compact. The proof is detailed and well presented.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.