ABSTRACT
The second chapter is titled “Numbers” and presents many proofs about this familiar concept in mathematics. It starts by discussing natural numbers and primes and presents two great proofs that there are an infinite number of primes. The narrative then progresses to integer, rational, real, and complex numbers. It proves that all these different types of numbers share their basic properties, which makes many applications of mathematics seamless and oblivious to the type of numbers being used. It explains the need for several basic properties of numbers, such as why the product of two negative numbers is positive. The most beautiful part of this section deals with determining how many numbers there are. It introduces the concept of a set on a basic level and shows that while there are infinitely many rational and real numbers, these are two “different kinds” of infinity.
