Definition:Number

There are five main classes of number:


 * 1) The natural numbers: $$\mathbb{N} = \left\{{0, 1, 2, 3, \ldots}\right\}$$;
 * 2) The integers: $$\mathbb{Z} = \left\{{\ldots, -2, -3, -1, 0, 1, 2, 3, \ldots}\right\}$$;
 * 3) The rational numbers: $$\mathbb{Q} = \left\{{p / q: p, q \in \mathbb{Z}, q \ne 0}\right\}$$;
 * 4) The real numbers: $$\mathbb{R} = ... $$;
 * 5) The complex numbers: $$\mathbb{C} = \left\{{a + i b: a, b \in \mathbb{R}, i^2 = -1}\right\}$$.

It is possible to categorize numbers further:


 * The set of algebraic numbers $$\mathbb{A}$$ is the subset of the real numbers which are roots of polynomials with rational coefficients;


 * The set of transcendental numbers is the set of all the real numbers which are not algebraic.