Hyperoperations and even bigger numbers | Data structures in Mathematics Math Foundations 179

A powerful approach to exploring big number arithmetic is to extend the notion of arithmetical operation. By considering hyperoperations starting with ,x,^ and then triangle, square etc we can ramp up arithmetic considerably. We can in fact inductively define an operation *_k for any natural number k. But then an interesting new possibility emerges, which opens up a whole new world of arithmetic--a rather lofty and hard to comprehend world, to be sure! We can consider a diagonal limit operation. This video is an introduction to the remarkable successor limit hierarchy which allows us to go far beyond our usual arithmetic! But don’t worry, we don’t actually get to infinity. That’s because there is no such place. ************************ Screenshot PDFs for my videos are available at the website . These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers c