Algebraic irrational

There are a few special classes of irrational numbers. An algebraic irrational is a zero of a polynomial of finite degree with integer coeflBcients. Since /2 is a zero of — 2 = 0, it is certainly algebraic. Cantor proved that the set of algebraic irrationals is countable (Dunham (1990)). 

The numbers that are not rational numbers are called irrational numbers. Algebraic irrational number include square roots of rational numbers, cube roots of rational numbers, and so on, which are not themselves rational numbers. All of the rest of the real numbers are called transcendental irrational numbers. Two commonly encountered transcendental irrational numbers are the ratio of the circumference of a circle to its diameter, called n and given by 3.141592653 , and... 

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