📝 SummarXiv

Abstract

I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard theories of summation and integration. This has implications in statistics (helping us work with distributions whose mean or variance is infinite), decision theory (allowing comparison of options with infinite expected values), economics (allowing evaluation of infinitely long streams of utility without discounting), and ethics (allowing evaluation of infinite worlds). There are even implications for finite cases, as the ability to handle these infinities undermines a common argument for bounded utility and the discounting of future utility.