Champernowne Constant is Transcendental

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Theorem

The Champernowne constant:

$0 \cdotp 12345 \, 67891 \, 01112 \, 13141 \, 51617 \, 18192 \, 02122 \ldots$

is transcendental.


Proof


Historical Note

The transcendental nature of the Champernowne constant was demonstrated by Kurt Mahler in 1937: Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen (Proc. Konin. Neder. Akad. Wet. Ser. A Vol. 40: 421 – 428).


Sources