### Transcendental number

A transcendental number has infinitely many decimal digits, and there never evolves a pattern that repeats itself.

##### Explanation

Numbers are an invention of men. Nature works without them. Everybody knows integers. Even a small child quickly learns how to count. There are also irrational numbers, complex numbers, etc. However, some phenomena cannot be expressed with these numbers. Then you may need transcendental numbers.

The most famous transcendental number is π. This number describes the ratio between the circumference and the diameter of a circle. The value is π = 3.1415…

Another famous transcendental number is *e*. You need this number if you want to calculate how bacteria multiply, or if you want to know how radioactive radiation decreases. The value is *e* = 2.7182…

Transcendental numbers are calculated by infinite series. The longer you calculate, the more accurate the number will be, and you can continue forever ... The amount of transcendental numbers is uncountable infinite, which means there are more transcendental numbers than integers.

##### Additional Information

The French mathematician Joseph Liouville proved in 1844 that transcendental numbers exist.