An Outcome of the de Finetti Infinite Lottery is Not Finite

Burock, Marc (2006) An Outcome of the de Finetti Infinite Lottery is Not Finite.

Abstract

A randomly selected number from the infinite set of positive integers—the so-called de Finetti lottery—will not be a finite number. I argue that it is still possible to conceive of an infinite lottery, but that an individual lottery outcome is knowledge about set-membership and not element identification. Unexpectedly, it appears that a uniform distribution over a countably infinite set has much in common with a continuous probability density over an uncountably infinite set.