Frank Blog

Welcome to Frank Blog, written by @keith_ps AKA Keith J. Bauer.
Why is it named Frank Blog? Well—

Contents

• Why n + 1 element sets are rank n simplices: https://frank-9976.github.io/simplices.html
  These are a collection of observations I've had about how sets with n + 1 elements have often wanted to be rank n simplices in my experience. Now I have a link to share when I want to explain what I mean by this!


• Proof that quasigroup midpoint algebras are averaging operations over Z[1/2]-modules: https://frank-9976.github.io/midpoint.html
  I literally wrote this just to justify my edit to this page on nlab: https://ncatlab.org/nlab/show/cancellative+midpoint+algebra
  It's quite beautiful math though, so I am proud of my work here.


• How to take quotients of monoids: https://frank-9976.github.io/quotient_monoids.html
  If you are not universal-algebra-pilled like me, you might have no idea that this is even a thing. This is my attempt to shine a light on this beautiful subject. Or more accurately, now I can link this whenever I want to introduce someone to quotient monoids.


• My first blog post: https://frank-9976.github.io/first_post.html
  This was the first thing I ever felt the need to make a blog for. I don't think I will ever update this but I am keeping it around for sentimental reasons. Just keep in mind I regret a few choices I made here. After writing the bulk of it, I did find someone who had similar ideas, so here is a link to his paper because I think it is really cool. His paper is also where I found K.R Matthews and G.M Leigh, which in my opinion is a really underrated result about collatz-like problems.