The Essential Dichotomy Underlying Mathematics Data Structures Math Foundations 185

Summary

Addition, multiplication and exponentiation are just the first three arithmetical operations on a fascinating ladder of operations ... In this video and the next, we review and extend the successor-limit hierarchy. This is a mysterious ladder of arithmetical ... The anti operation provides us with a technical tool to work with multisets in which objects occur with negative multiplicities. 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 start this video by reviewing some standard uses of numbers: to allow us to determine sizes of sets/msets, to determine the ... We introduce the idea of the complexity of a natural number: a measure of how hard it is to actually write down an arithmetical ... A powerful approach to exploring big number arithmetic is to extend the notion of arithmetical operation. By considering ... In this video we introduce the idea of the anti of a In this video we continue bringing the notions of vexels, polynumbers and Hindu Arabic numbers together. After a careful look at ... This video is a continuation of MF181, in which we reviewed and extended the successor-limit hierarchy of very big arithmetical ... It is time to turn our gaze back to the true The successor - limit hierarchy exhibits interesting kinds of self-similarity, along the lines of fractals. One manifestation of this ...