Infinity does not exist

There is an interesting article in Quanta `Is Infinity Real?’ and this references an article in Discover `Infinity Is a Beautiful Concept – And It’s Ruining Physics’. I like both articles because they support my point about theories of statistical inference that anytime infinity is used we must be sure that we are in effect approximating something finite. This gets rid of a lot of paradoxical behavior. If you have a counterexample and it only holds when something is infinite, then you really don’t have a counterexample. A simple example of this occurs with the MLE. When the sample space and parameter space are finite, the MLE is consistent but of course there are many counterexamples where the MLE is not consistent and these depend intrinsically on infinity. So is the problem with the MLE or with the models? Certainly the mathematics is often much nicer when use is made of infinity, and that is fine by me, just don’t believe that models containing infinities represent the truth.