The following is a free book for anyone interested in learning about real numbers.
About the book (by the author)
In these notes we will deal with two major topics: mentioned in the title. To study real numbers, it is necessary to know the properties of rational numbers and to understand integers.
We will therefore begin in Chapter 1 by discussing the algebraic properties of integers and rationals. Since the main difference between rational and real is reflected in order, we will also study the properties contained in the order of rational.
In Chapter 2 we will study reality. Emphasis will be placed on using the highest attribute to show some of the important properties of R.
Chapter 1 has another purpose. We want readers to experience, perhaps for the first time, formal symbolic evidence. That is, logical arguments are presented sequentially where each proposition in evidence must be strictly justified.
We will do this only in the part of Chapter 1, the rest of the text will be written in the usual style of mathematics, which, although rigorous and formal, does not follow that rigorous plan of demonstration of symbolic logic.
The second topic we want to address is the concept of infinity. To do this naturally one must first study the functions. This in itself is a very important objective, as functions are an essential tool for all math courses.
In Chapter 3 we give a brief introduction to binary relations so that the concept of function can be presented as a specific type of binary relation.
Finally, in Chapter 5 we study the concept of cardinality. We want readers to be familiar with the basic properties of infinite sets, especially to be able to distinguish between measurable sets, and to know that lines are not the same size as rational numbers.
Content (subject)
- Rational number
- Real numbers
- Relationships
- Tasks
- Cardinality
Information sheet
Year: 2011
Editor: University of the Andes
English: Español
Size: 916 KB
License: Pending review
About OpenLibra
OpenLibra strives to bring together as many free publications as possible under one platform. This should be taken into account and indicates a series of risks in terms of content that we would like to inform our users about.
In OpenLibra, books are the sole responsibility of their authors. This means that OpenLibra cannot guarantee the validity of its content.
This may be of interest to you
Frequently Asked Questions
What is a free library?
This means that all the books they produce are licensed under one of the many free licenses that exist, and therefore, authors authorize its reproduction and redistribution.
So are all the books in this library free?
Yes; At least for its digital version. Many authors, in addition, offer a printed version (either directly or through a regular commercial circuit) for which they may charge what they deem appropriate.
But some of the books in the library are copyrighted.
Copyright and free licenses are not mutually exclusive. In fact, the latter relied on earlier legislation to grant copyright and distribution rights. That is why every work under free license has the copyright which guarantees the will of its author. What matters is what copyright allows in the context of licensed work.
Well, I’ve seen a book around that has copyright and ‘all rights reserved’.
Sure; In these cases, it is most common for the publisher to return the exploitation rights to the author. This is usually accompanied by technical regulations after a reasonable time has elapsed or, for example, when printed editions have run out and are not intended to be reissued. Once the authors are back in control, they can leave their work in the public domain or redistribute it for free to republish their work.
If the books are free and free, can I do what I want with them? Can I print, translate and / or sell it?
No; You cannot do what your license does not allow. As explained in the link above, some licenses only allow non-profit downloads and redistributions. For example, if you want to translate a work and edit it in a normal way, some authors will have to pay you the respective rights.
Download the book
If you are interested in the topics, we leave you a download link below.
Find free courses and books in our telegram, as well as Udemy coupons.
0 Comments