10.1 Numbers
There are five famous classes of numbers that one has to know in order to become adept in mathematics:
- natural numbers, denoted by ℕ,
- integers, denoted by ℤ,
- rational numbers, denoted by ℚ,
- real numbers, denoted by ℝ,
- and finally, complex numbers, denoted by ℂ.
These classes increase in order, that is,
In this section, we are going to concern ourselves with the first four. (Complex numbers will get their own chapter.)
10.1.1 Natural numbers and integers
Natural numbers are simply defined as
Sometimes 0 is included; sometimes it is not. Believe it or not, after a few thousand years, mathematicians still cannot decide whether or not 0 is a natural number. This problem might sound comical, but trust me, I have seen senior professors almost get into a fistfight upon debating this issue. For some people, this is a religious question.
I don’t particularly care, and neither should you. I propose using the more common and practical...
