To dig something out of my archives today, I offer the Zermelo-Fraenkel Axioms. This wrapped up the End 2016 A-to-Z. On the last day of 2016, I see; I didn’t realize I was cutting things that close that year. These are fundamentals of set theory, which is the study of what you can include and what you exclude from a set of things. For a while in the 20th century this looked likely to be the foundation of mathematics, from which everything else could be derived. We’ve moved on now to thinking that category theory is more likely the core. But set theory remains a really good foundation. You can understand a lot of what’s interesting about it without needing more than a child’s ability to make marks on paper and draw circles around some of them. Or, like my essays insist on doing, without even doing the drawings that would make it all easier to follow.
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