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2025-09-25 09:14:12

Evaluating the Infinite
Toby Ord
https://arxiv.org/abs/2509.19389 https://arxiv.org/pdf/2509.19389

Evaluating the Infinite
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 infi…