Transcendental Numbers

Studying irrational numbers revealed that there were two types of irrational numbers.

One type was called Algebraic Irrationals.

These were numbers like √2, √3 & ψ (phi) which are solutions to algebraic equations like x²=2 or x³=3.

The other type, which cannot be roots of algebraic equations, are called Transcendental irrationals or just Transcendental Numbers.

π and e which were discovered to be limits of totals of infinite series of fractions were also discovered to be transcendental numbers.

As the famous mathematician Euler put it, “They transcend the power of algebraic methods.”

Transcendental numbers are a strange kind of numbers.

It is known that they are more numerous than any other kind of real numbers. Like Real numbers, they are also uncountable.

But very few transcendental numbers have been identified as "unique" like π and e.

It is very difficult to prove that any numbers is transcendental.