$\newcommand{\I}{\mathcal I}$$\newcommand{\N}{\mathbb N}$$\newcommand{\Q}{\mathbb Q}$$\newcommand{\R}{\mathbb R}$In this post I’m going to explore partitioning the unit interval $\I := [0,1]$ into uncountably…
In this post I’m going to prove that the following four statements are equivalent given the ZF axioms: (1) Hausdorff…
Here I’m going to go through one common proof of the following result: Theorem: assuming Zorn’s lemma, every vector space…
In this post I’m going to prove the Schroeder-Bernstein theorem and then discuss an order on the class of all…
In the previous post I looked at binary relations on finite sets; in this post I’m going to prove a…
There are a lot of times when I encounter an unordered set but then end up working with a matrix…
$\newcommand{\X}{\mathscr X}$$\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…