A New Set Theory for Analysis
Round 1
Reviewer 1 Report
See the attached report.
Comments for author File: 
Comments.pdf
Author Response
The reviewers remarks are greatly appreciated and have been great help in clarifying, and correcting some errors that were due to the authors carelessness.
The manuscript has been revised to eliminate ambiguous notations and confusion that may arise from the use of symbols. A new range of symbols has been used in most cases to clarify and make clearer several concepts. No symbols have been used without first defining them. The notations are kept consistent throughout and we adopt convention of using lower case $x,n,m$ for representing numbers, and the upper case X,N,M represents the corresponding set number.
Most sections have been either intervened or rewritten, although the logical order of the development has remained the same, for the most part. Below we give a section by section review of the changes made to the original version.
Changes have been made to the Introduction, in order to provide definitions of set numbers early on and avoid confusion regarding the different classes of set numbers.
The order relation has been given a new symbol, to avoid confusion with the usual order of numbers.
The sections for supremum and infimum of these sets has been rewritten, and we avoid using any undefined objects.
Reviewer 2 Report
This paper is well written and offers a very interesting presentation of the real number system based on the fact that R is isomorphic to 2N in terms of structure (not only cardinality)..
Author Response
Thank you for your review and time. I greatly appreciate it and will try to make some improvements.
Round 2
Reviewer 1 Report
The author marginally improved the Introduction taking into account part of my remarks.
The paper could be considerably improved by a careful reformulation but if the author wishes to present it as it stands, I'm not opposing any longer. Nevertheless I continue to think it is a pity because the results deserve a better presentation.
At least correct some Latex typos (for instance line 48).
Author Response
A slightly modified version is submitted with the following changes:
Latex errors and typing mistakes were identified.
In the paragraph for "roots" we changed the notation for order of set numbers, because it was not changed in the first revision.
In the paragraph of "logarithms" a statement was clarified.
The abstract has been modfiied.
Confusing or ambiguous remarks have been dealt with, to the best of the authors ability.
