Algebraic Number

When a number is not algebraic, it is called transcendental.It is known that π (pi) and e (Euler's number) are not algebraic, and so are transcendental.

Definition

To be algebraic, a number must be a root of a non-zero polynomial with rational coefficients.

All algebraic numbers are computable and so they are definable.The set of algebraic numbers is countable. Put simply, the list of whole numbers is "countable", and you can arrange the algebraic numbers in a 1-to-1 manner with whole numbers, so they are also countable.

All rational numbers are algebraic, but an irrational number may or may not be algebrabraic.What about the square root of 2?

According to the definition it is algebraic (and not transcendental).

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