In this post I’m going to prove that the following four statements are equivalent given the ZF axioms: (1) Hausdorff…
$\newcommand{\e}{\varepsilon}$In this post I’m going to prove the intermediate value theorem (IVT), Darboux’s theorem, and introduce the Conway base 13…
Here I’m going to go through one common proof of the following result: Theorem: assuming Zorn’s lemma, every vector space…
In this post I’m going to prove the Schroeder-Bernstein theorem and then discuss an order on the class of all…
In the previous post I looked at binary relations on finite sets; in this post I’m going to prove a…
There are a lot of times when I encounter an unordered set but then end up working with a matrix…
$\newcommand{\X}{\mathscr X}$$\newcommand{\Y}{\mathscr Y}$$\newcommand{\pow}{\mathcal P}$Let $f : \X \to \Y$ be a function between non-empty but otherwise arbitrary sets $\X$ and…