Chapter 5 A brief digression on numbers
The "natural numbers" are what would happen if someone were to spontaneously break out counting: (and so on). These are called the "natural numbers" and denoted as . To say a number is a natural number, we can say that it is in the set of natural numbers, and can write this as (where is our number).
From the natural numbers, a logical next step is the set of "integers". These are just the numbers (going infinitely far in either direction).
After this, there are the "rational numbers". A "rational" number is a number which can be written as . So or or or or or are all rational numbers. This set can be denoted using the symbol .
Some numbers aren’t rational, however. or are "irrational" numbers 11 1 There’s a proof of this in the proof section.. The "real" numbers, , include the "irrational" numbers (as well as some other numbers). If we think of the rational numbers on a number line, then the real numbers are (informally) an attempt to \sayplug the gaps between the rationals.
Note that .