Towards the construction of a normal Lüroth series
A. Boks · Research Repository (Delft University of Technology) · 2009
In this thesis we present a Lüroth series A that we conjecture to be normal. The series A is constructed by concatenating elements from a probability tree that enumerates all finite Lüroth series. We give an outline for a proof of the normality of A in four steps, of which we will prove three. Regarding the fourth step, which we cannot prove yet, we will state some remarks on its plausibility and a possible strategy for a proof. To conclude we describe the possibilities of extending the construction presented to other Generalized Lüroth Series and compare the mentioned construction to constructions for normal numbers in other expansions.