Algebra/Algebra

Numbers:

The Natural Numbers:

$$ \ N = \lbrace 1, 2, 3, ..., n, n + 1, ... \rbrace $$

The Whole Numbers:

$$\ W = \lbrace 0, 1, 2, 3, ..., n, n + 1, ... \rbrace $$

The Integers:

$$\ Z = \lbrace 0, \pm 1, \pm 2, \pm 3, ..., \pm n, \pm (n + 1), ... \rbrace $$

The Rational Numbers:

$$\ Q = \lbrace \ \frac{a}{b} \ \vline \ a,\ b \in Z,\ b \ne 0 \rbrace $$ numbers that can be expressed as quotients, i.e. $$\ 2.1 = \frac{21}{10},\ \therefore 2.1 \in Q $$

Irrational Numbers:

$$\ I = \lbrace a\ \vline\ a \notin Q \rbrace $$ examples: $$ \sqrt{2}, \sqrt{3}, \sqrt{10}, \pi, e $$

Transcendental Numbers:

$$\ T = \lbrace $$ Transcendental Numbers $$\ \rbrace $$ examples: $$\ \pi, e$$

$$\ R = \lbrace $$ all the numbers $$\ \rbrace $$

The Complex Numbers:

$$\ C = \lbrace a+bi\ \vline \ a,b \in R, i = \sqrt{-1} \rbrace $$