Purchase Solution

# Bounded Real Sequences and Metrics

Not what you're looking for?

Let X be the set of all bounded real sequences ... (SEE ATTACHMENT FOR COMPLETE QUESTION) ... For points x = {x1,,x2,x3...} and y = {y1,y2,y3...} in X define:
d(x,y) := SUP |xk-yk|.
(k less than or equal to 1)
Prove that d is a metric (remember to explain why d(x,y) is finite!)

(Please explain in your own words how the proof works. If you use a theorem, please state what it is and if possible, where you got it).

##### Solution Summary

Bounded Real Sequences and Metrics are investigated.

##### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Solution:

First of all, we will show that d(x,y) = finite.
Let Mx >0 so that

Now, we need to check all the axioms of the metric:
1)
This is obvious because of the properties of module:
...

##### Graphs and Functions

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

##### Probability Quiz

Some questions on probability