There are different types of numbers, for instance:

**Z**- Integers - whole numbers: ... -3, -2, -1, 0, 1, 2, 3 ... both positive, zero and negative.- - Real numbers - numbers which are continuous such as when we are representing points along a line - On this site I will sometimes use the term 'Scalar' to mean 'Real' numbers although strictly the term should be used when scaling a vector - In computer programs real numbers have a finite length and may have decimal point and/or exponent this allows us to approximate most real numbers but it is only an approximation.
**Q**- Rational numbers - Integers and fractions where numerator and denominator are integers.- Radical Integers - The integers plus any combination of addition, subtraction, multiplication, division and root extraction.
**Q**^{alg}- The root of a**Z**-polynomial - A complex number made up more than just radical integers although it is closed under sum, difference, product, quotient and n^{th}root. (The solutions to**Z**-polynomials are discussed on this page).- Modulo 'n' numbers.

There are also compound number where each element may be one of the above types.

**C**- Complex Numbers - numbers with real and imaginary parts.**H**- Quaternion - Complex number whose elements are complex numbers.**O**- Octonion - Quaternion whose elements are complex numbers.- Vectors - one dimensional arrays of numbers.
- Matrices - two dimensional arrays of numbers.

and these numbers may be coded in different ways:

- binary
- octal
- decimal
- hexadecimal

Unless otherwise specified we usually assume that numbers are decimal.

## Infinity

Infinity is a number bigger than any real number

Georg Cantor, the great mathematician whose work proved to be the foundation for much of the 20th-century mathematics. He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.

He discovered a whole hierarchy of infinities.

He devised the continuum hypothesis but failed to prove or disprove it.