Interpreting Infinite Numbers

Abstract

The mathematical concept of infinity, in the sense of Cantor, is rather far from applied mathematics and statistics. These fields can be linked. We comment on the properties of infinite numbers and relate them to some operations with random variables. The existence of statistical parametric models can be studied in terms of cardinal numbers. Some probabilistic interpretations of Gödel’s theorem, Turing’s halting problem, and the Banach-Tarski paradox are commented upon, as well as the axiom of choice and the continuum hypothesis. We use a basic but sufficient mathematical level.