These are the numbers that are not algebraic. There is no integer coefficient polynomial from which they are root.

The number Pi, for example, is a transcendent number because it cannot be obtained as the root of any integer coefficient polynomial.

Transcendent numbers are infinite and there is much more than algebraic numbers (which are those that can be obtained as the root of an integer coefficient polynomial). Root of 3 is an algebraic number, since it is a solution of equation x^{2}-3=0.