Elementary mathematics A Modern Approach

From the preface:
This book gives the non-science college student an elementary yet
comprehensive introduction to the structure of the real number
system and its subsystems and to related topics, including
elementary set theory, systems of numeration, elementary number
theory, and mathematical systems. In large measure, the book
follows the recommendations for the Level I college course in
number systems proposed by the Committee on the Undergraduate
Program in Mathematics (CUPM)...

My own commentary:
Well, if you do really want to have a philosophical introduction
into the universe of mathematics, I do recommend William
Dunham's The Mathematical Universe. This is really fine
work. But, sadly, I have no any of the book. :(

But, if you want to have a technical introduction, then, this
book is perfectly suitable for your situation.

Then, if you have finished this book, you can continue working
on Elementary Concepts of Mathematics, second edition.

Table of contents:
1. Elementary set theory
2. Systems of numeration
3. The natural numbers and the whole numbers: addition and multiplication
4. The natural numbers and the whole numbers: substraction,
division and elements of number theory
5. The nonnegative rational numbers
6. Decimals and percent
7. The rational numbers and the real numbers
8. The structure of mathematical systems