Algebra/Algebra

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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