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:
$\ Q=\lbrace \ {\frac {a}{b}}\ \vline \ a,\ b\in Z,\ b\neq 0\rbrace$ 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:
$\ C=\lbrace a+bi\ \vline \ a,b\in R,i={\sqrt {-1}}\rbrace$