On Randomness and Infinity
Grégory Lafitte · 2002
In this paper, we investigate refined definitions of random sequences. Classical definitions have always the shortcome of making use of the notion of an algorithm. We discuss the nature of randomness and different ways of obtaining satisfactory definitions of randomness after reviewing previous attempts at producing a non-algorithmical definition. We present alternative definitions based on infinite time machines and set theory and explain how and why randomness is strongly linked to strong axioms of infinity .