(1)

where the s are integers and satisfies no similar equation of degree , then is an algebraic number of degree . If is an algebraic number and , then it is called an algebraic integer.

Examples of algebraic numbers and their degrees are summarized in the following table.

constant	degree
Conway's constant	71
Delian constant	3
Freiman's constant	2
golden ratio	2
Graham's biggest little hexagon area	10
hard hexagon entropy constant	24
logistic map 4-cycle onset	2
logistic map 8-cycle onset	12
logistic map 16-cycle onset	120
plastic constant	3
Pythagoras's constant	2
silver constant	3
silver ratio	2
tetranacci constant	4
tribonacci constant	3
Wallis's constant	3

If, instead of being integers, the s in the above equation are algebraic numbers , then any root of

(2)

is an algebraic number.

If is an algebraic number of degree satisfying the polynomial equation

(3)

then there are other algebraic numbers , , ... called the conjugates of . Furthermore, if satisfies any other algebraic equation, then its conjugates also satisfy the same equation (Conway and Guy 1996).

Any number which is not algebraic is said to be transcendental. The set of algebraic numbers is denoted (Mathematica), or sometimes (Nesterenko 1999), and is implemented in Mathematica as Algebraics. A number can then be tested to see if it is algebraic using the command Element[x, Algebraics].