Numeric and counting systems

Position based

 * Hindu-Arabic numerals

Positionless

 * Cyrillic numerals
 * Hebrew numerals
 * Roman numerals

Counting systems

 * binary
 * octal
 * decimal
 * dozenal
 * hexadecimal

Number classes

 * natural number
 * whole number
 * real number
 * transedental number
 * fraction
 * imaginary number
 * algebraic number
 * computable number
 * definable number

Types of infinity

 * Aleph number