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