The power of simple examples in advanced math

In which we play with numbers and pretend to do advanced math. **Notes and Further Discussion** 1. Honestly I don’t remember where I read this, I thought I read it in the article "Rosetta Stone" by John Baez, if any of you can point me towards the source I would love that. 2. The categories Div and Nat mentioned in the video are examples of poset categories. A poset is a set where we draw an arrow from a "smaller" element to a "larger" element, and no arrow when the elements are "incomparable". In this case, the product is the "meet of the elements" and the coproduct is called the "join". 3. Proof of the first identity in the video: https://numerodivergence.wordpress.com/2025/04/30/gcds-and-lcms-help-us-understand-category-theory/ **Clarifications and Corrections** None yet! **Acknowledgements** 1. Please check out @josephnewton 's video: https://www.youtube.com/watch?v=4uJLvby7K9Y 2. Book cover for "Category Theory in Context" **Music** The outro song is performed by me on my Uke. **Production** All art was made on PowerPoint. This video was definitely one of those where I did less animations and focused more on just drawing a bunch and writing formulas. **End Notes** There is a certain charm to bringing "advanced mathematics" down to a level that is understandable by all. Even though this method is limited in what it lets you do, the fact that it lets you do anything *at all* is something worth talking about. I only remember seeing the products and coproducts explanation somewhere, and so I made an active effort to prove some identities with this interpretation so as to make it "more valuable". This is what math is all about, just little things adding up to something marvelous, in the most literal sense of the word. Solidarity forever.