Complexity And Hyperoperations Data Structures Math Foundations 174

Summary

This is a sobering and perhaps disorienting introduction to the fact that arithmetic with bigger numbers starts to look quite different ... A powerful approach to exploring big number arithmetic is to extend the notion of arithmetical operation. By considering ... Here we go back to the first videos in this series and recast that discussion in a more solid direction by utilizing our understanding ... We are starting to appreciate the fundamental importance of the framework of Nat, the primitive natural numbers as the basic ... Here we look at a somewhat unfamiliar aspect of arithmetic with natural numbers, motivated by operations with multisets, and ... It is time to end the delusion which pervades modern 20th century style The anti operation provides us with a technical tool to work with multisets in which objects occur with negative multiplicities. We set up integer arithmetic in a novel fashion, using the essential trichotomy of a mark, an anti-mark, and nothing. The idea of an ... Matrix theory is just a shadow of the more fundamental and far-reaching maxel theory. In our last video we introduced maxels from ...