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What does it mean if a number is transcendental?
It means that it is not algebraic... that is, it is not the root of a polynomial expression with rational coefficients.There are infinitely more transcendental numbers than algebraic numbers, but only a few are of any practical importance... most prominently pi and e, the base of the natural logarithms.All (real) transcendental numbers are irrational, but not all irrational numbers are transcendental. For example, the square root of two is irrational, but it is not transcendental as it is a root of the equation x2 - 2 = 0, a polynomial expression with rational coefficients.
Why all irrational numbers are not surd?
There are transcendental numbers such as pi, e, phi. The fact that they are transcendental means that they are not solutions of non-trivial algebraic polynomials with rational coefficients. There is, therefore, no surd form for such numbers.
What is pi an example of what kind of numbers?
Pi belongs to the sets of real numbers, transcendental numbers and irrational numbers.
What are the four kinds of real numbers?
Integers (eg 5), rational numbers (eg 7/9), irrational numbers (eg sqrt(3), transcendental numbers (eg π).
Ratio of circumference of a circle to its diameter?
The ratio is pi, a transcendental number, which is a subset of irrational numbers. pi is approximately equal to 3.14159
