Rational Numbers: Natural Numbers: 0 and Positive Numbers: Fractions (True Fractions and False Fractions) (Infinitely Cycling Decimals), Integers.

Negative number.

Irrational number: infinite cyclic decimal.

imaginary number

Common factor, common multiple, prime number, composite number ...

Logarithm, reciprocal ...

Well, does the function count? Trigonometric functions, those ...

That's all I can think of,