# Real Analysis

My questions are from sections 5 and 6.

Since most of questions are from section 6, I will just just attach reference_6 pdf file with my question sheet. I think you actually have all of my reference copies.

This is the same on-line link to my textbook that I sent you earlier today:

http://books.google.com/books?id=z8IaHgZ9PwQC&pg=PA72&dq=unique+solution+contraction+mapping&lr=#PPA65,M1

My questions are from sections 5 and (mainly)6 for this posting.

© BrainMass Inc. brainmass.com October 9, 2019, 10:59 pm ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-functions-240118

#### Solution Preview

The explanations are in the attached text in two formats.

Question 1:

Proof that a bounded set {S⊂R┤| x<M ∀x∈S} has

〖sup〗┬(x∈S)〖|x|〗

Let us start from the closure [S] and consider the Corollary at the bottom of page 51 saying that every closed set on the real line can be obtained by removal of a countable system of pair-wise disjoint open intervals from the line (a typo in the text of the book misses the word "open"). Let us consider this system of intervals and note that since there is the bound x<M , any point to the right of M must be removed, so there is a right-most interval (a,∞) in the system of removed ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer real analysis.