Number Theory

Numbers are defined by the mathematical units (not numbers) 1 and i (the real and imaginary units), and are typically put into number systems when they need to be stored. There exists various classes of numbers:

1. Natural Numbers
2. Whole Numbers
3. Rational Numbers
4. Irrational Numbers
5. Imaginary Numbers
6. Complex Numbers

Number types (as sets)

$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$

$\mathbb{I} \cup \mathbb{R} = \emptyset$

$\mathbb{C} \cup \mathbb{R} = \emptyset$

See set theory.