Purchase Solution

Countable Sets and Limit of Sequence of Functions

Not what you're looking for?

Ask Custom Question

Show that there is a countable set F of functions of form

x--->a_0 + a_1cosx + a_2cos(2x) + ... +a_ncos(nx)

such that every continuous real-valued function on [0,pi] is the uniform limit of a sequence of functions (f_n) in F.

Attachments
Purchase this Solution

Solution Summary

The Solution finds a countable set and the limit of sequence of functions.

Purchase this Solution


Free BrainMass Quizzes
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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

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

Multiplying Complex Numbers

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

Probability Quiz

Some questions on probability