I want to understand how number system evolved from scratch.
I am looking for a book which starts with natural numbers, explains their origin, explains how addition and multiplication is defined on them rigorously. Then how integers, rationals were developed, operations on them, and finally reals. I want to understand all this very rigorously.
I would like to have suggestions for reference books.
Thank you.
P.S. The reason behind asking this question was, from recently I have started feeling something unreal about numbers. I mean when I think about decimals whether recurring or non-recurring, finite or infinite, irrationals like π or e, I just get blank and keep thinking, what these numbers actually are? What they represents? How they arrive? And many such questions. I don't know why and how these started but I am feeling very uncomfortable dealing with numbers. Honestly I am very very serious about this issue of mine and that's why wanted to understand evolution of number system. I thought there might be some books about this construction.
In the comments, you say you want a rigorous treatment, not a historical one.
There is a standard answer to this question, "Foundations of Analysis" by Landau. I've only ever glanced at it, and what I saw didn't make me want to look at it any further.
I have to say, I've never seen a treatment of the natural numbers I liked in an algebra or analysis book.
You can get a more sensible treatment of N, based on cardinals, in a set theory book like "Introduction to Set Theory" by Jech and Hrbacek, though they leave some details for you to work out as exercises.
Jacobson's "Basic Algebra I" has a presentation of N I like less, but it has the steps from N to Z and from Z to Q. The step from Z to Q can be found in any abstract algebra book under "field of fractions of an integral domain".
You said you'd read the construction of R from Q as Dedekind cuts, so I'm not sure what more you'd like than that.