# derive-it.com

• ## Irrational Numbers

Are rational numbers the only numbers? The continuity of real numbers is an assumption in the Cantor-Dedekind axiom . The idea of continuity brings up the possibility of a different type of number called an irrational number that is, simply, not a rational number. So, if a number is not a rational number, it is…

• ## Definition of a Sequence

The title of Section 2 in book  is Sequences of rational numbers. At the beginning of this section, a definition is provided for a sequence, and I quote it here. Definition. If, by means of any suitable process of construction, we can form successively a first, a second, a third, … (rational) number and…

• ## Reaching for that Number Theory book (Part I)

I now turn to number theory, because this field seems like a solid foundation for mathematics and physics. I start with Chapter 1 of the esteemed book, Theory and Application of Infinite Series . The title of Chapter 1 is “Principles of the theory of real numbers.” Section 1 is called “The system of rational…