https://snowlesswinter.neocities.org/posts/ Recent content in Posts on snowlesswinter.com Hugo -- gohugo.io en-us Sat, 26 Mar 2022 12:21:26 -0500 https://snowlesswinter.neocities.org/posts/jech3/ Sat, 26 Mar 2022 12:21:26 -0500 https://snowlesswinter.neocities.org/posts/jech3/ The final pages of the first chapter of Set Theory expound on a few more ZF axioms. The axiom of power set Let’s kick off by defining subset. We say $u$ is a subset of $X$ iff $\forall z (z \in u \implies z \in X)$. This is written as $u \subset X$. A proper subset of a set $X$ is a subset of $X$ that isn’t equal to $X$. https://snowlesswinter.neocities.org/posts/classes/ Wed, 16 Mar 2022 12:42:07 -0600 https://snowlesswinter.neocities.org/posts/classes/ Our last post took us through the axioms of ZF and explored the first two in detail. This post explores the schema of separation and the notion of classes in ZF. Schema of separation Recall that the fourth axiom of ZF is the schema of separation, which states that if $P$ is a predicate with parameter $p$, then for any $X$ and $p$ there exists a set $Y = \{u \in X \mid P(u,p) \}$. https://snowlesswinter.neocities.org/posts/jech1/ Sat, 26 Feb 2022 00:00:00 +0000 https://snowlesswinter.neocities.org/posts/jech1/ Introduction Set theoretic ideas were banging around the mathematical world for a long time, but Georg Cantor and Richard Dedekind are usually credited as the pro- genitors of what we call naïve set theory. Naïve set theory doesn’t refer to one theory but rather to a collection of informal, natural language descriptions of set theory. It wasn’t long after these descriptions emerged that fundamental problems inherent in them–including but not limited to famous Russell’s paradox–also emerged. https://snowlesswinter.neocities.org/posts/hello/ Tue, 22 Feb 2022 00:00:00 +0000 https://snowlesswinter.neocities.org/posts/hello/ Who are you? Nicholas Bergeron. I went to Vanderbilt from 2016-2020 where I picked up a B.A. in math with minors in scientific computing and European studies. In 2021 I went to big tech but didn’t like it there, so I came to Chicago to make a living tutoring. I plan to keep tutoring until I begin grad school in philosophy. What’s this website about? My main academic interests: philosophy of math, philosophy of logic, logic, and set theory.