Monday, May 19, 2014

Liouville's number 0.110001000000000000000001000 ...

1! = 1      (one factorial)
2! = 2x1 = 2   (two factorial)
3! = 3x2x1 = 6
4! = 4x3x2x1 = 24
5! = 5x4x3x2x1 = 120


Liouville's number is a decimal that is all 0s except for the decimal places that correspond to a factorial, where thee is a 1 instead.  So there is a 1 in the 1st, 2nd, 6th, 24th, 120th, 720th. etc place.

Since the decimal never forms a repeating pattern, it is not rational, meaning it can not be written as a fraction with a whole number over a whole number.  It is also transcendental, meaning it can not be the solution to an algebraic equation.

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