Three-Toed Sloth

Problems in the Doctrine of Chances

Paradoxes and fallacies are fun teaching tools, and elementary courses in probability theory are well supplied with them. I have long thought that more advanced probability classes would be more palatable if we presented our students with more opportunities to go "Wait, that can't be right", and sink their teeth into something really just-plain-wrong. Happily, we now have about ten more such morsels to offer them:

Guang-Liang Li and Victor O. K. Li, "Inconsistencies in Current Theories of Real Numbers, Measure, Probability, and Stochastic Processes", math.GM/0606635

Abstract: Current theories of real numbers, measure, probability, and stochastic processes appear to be self-inconsistent. We exemplify the inconsistencies with Poisson processes, Markov chains, continuous random variables, the Lebesgue measure, and the Cantor-Dedekind theory of real numbers.

Anyone taking 36-754 from me next spring should expect to see sections 2 and 3 as assignments.

Enigmas of Chance