Purpose

This post aims at recapturing the main ideas of the formal proofs that I’ve read. It never tries to replace them. You may consult the references if you need any of them.

Some notations

Unless otherwise specified, all cardinalities here are infinite. Denote $\mathfrak{a} = \card{A}$, $\mathfrak{b} = \card{B}$ and $\mathfrak{i} = \card{I}$.

Sum

$\mathfrak{a} + \mathfrak{b} = \card{A \cup B}$ provided that $A \cap B =\varnothing$.

Product

$\mathfrak{a} \, \mathfrak{b} = \card{A \times B}$

Power

$\mathfrak{a}^\mathfrak{i} = \card{A^I}$, where $A^I = \lbrace f \mid f: I \to A \rbrace$ denotes the set of functions from $I$ to $A$.

I've chosen $I$ instead of $B$ to express the index set because this reminds me of an array of $(a_i)_i$ indexed by $I$.

Goal

To get Julia installed as a normal user on RHEL 6.

Motivation

“Julia talks like Python but walks like C.”

To do statistics more efficiently.

The compiled binaries often contain install scripts which put files to shared folders under /usr. Consequently, they have to be run as sudo privileges. That drove me to start this lengthy Julia compilation.

Installation

Without sudo privileges, I’ve chosen to compile Julia from source. I was too lazy to get the dependencies fixed. I just compiled it without GFortran and pkg-config under the ~/src folder.

Introduction

This article records my errors and difficulties encountered on the first day I came across Red Hat Enterprise Linux 7 in my school’s laboratory, as a normal user without sudo privileges.

The login screen was gdm, and the desktop environment was GNOME. IBus was used as the input engine.

Packages installed

The principal goal is to install tools that I usually use on RHEL without sudo permissions. To do so, I’ve downloaded the executable binaries or source code of these packages. As I wanted to focus on my studies, I prefer downloading executable binaries.

Statement

Slogan version

$$\sigma = \pi + \lambda$$

$\sigma$	$\pi$	$\lambda$
“sum”	“product”	“limit”
universe	nonempty	universe
complement		complement
countable union	finite intersection	disjoint countable union

A $\sigma$-algebra is a $\pi$-system and a $\lambda$-system, and vice versa.

Wiki version

A $\lambda$-system is a synonym of a Dykin system.

$$\mathcal{P} \subseteq \mathcal{D} \Longrightarrow \sigma(\mathcal{P}) \subseteq \mathcal{D}$$

Given a $\pi$-system contained in a $\lambda$-system. Then the $\sigma$-algebra generated by the $\pi$-system is also contained in the $\lambda$-system.

[Read More]

Update: I suggest reading a newer tutorial for setting up your custom API server that works with GitHub Apps. The package maintainers suggest hosting your own API server.

Goal

To host an instance of Staticman v3 server on Heroku.

This post involves server-side setup of the commenting system. If you simply want to have a taste of this system on GitLab, you may try my demo GitLab Page.

I try to address some concerns about this API service in the introduction of this series to keep this page focused on the technical aspects of my customizations against staticman/dev branch.

Background

While making changes to a theme for a static site generator, I changed files under a Git submodule included in the repo for my blog. (e.g. themes/beautifulhugo) That’s ideal for local testing, but not for version control. As a result, I cloned the repo for the theme to a directory separate from the one for my bloge (say, ~/beautifulhugo), and commit the changes there, then performed a Git submodule update so as to make the workflow clean.

Background (TL;DR)

While setting up the new version of Staticman for my demo GitLab pages, I’ve read developers’ documentations, setup guide and some community blog posts so as to come up with my own guide. It’s originated and inspired from a variety of sources, and refined according to hours of testing. Consequently, despite the original intention to keep things simple, I’ve finally come up with a post with over a thousand words.

To pass my ideas in this post to visitors, it’s better that they have an overview of the contents before actually looking into the details. Therefore, a table of contents is nice-to-have feature for this blog.

Update: I suggest reading a newer tutorial.

To keep focused on the technical setup, please refer to the introduction of this series for the reasons of choosing Staticman and GitLab.

Goal

To set up unauthenticated commenting system on GitLab pages.

This post aims at providing a walkthrough to the GitLab repo setup. If you want to host your own Staticman API instance, you may refer to the next post in this series.

I put some “why” questions here so as to keep focus on the technical setup of the GitLab repo and the optional Staticman API server.

Why static blogs instead of dynamic ones?

• quicker loading time
• better reliability (can handle more request)
• no database needed
• greater control on content, styles and layout

Why static comments?

• allow feedback from visitors
• site owner owns the comment locally (unlike WordPress, Facebook, Disqus, etc)
  • no remote database needed, so no need to worry server errors from third-party commenting services.
  • greater control over the rendering of the comments (allow additional features such as Markdown syntax, and $\KaTeX$ support)
  • more accessible since static comments are incorporated as HTML elements into the post. No JavaScript is required to retrieve the comments, contrary to most third-party commenting services.

Before Staticman’s deployment, another commenting system called Pecosys was already available. However, it’s less convenient to handle visitor’s requests as emails.

Background

My churches are going green.

Problem

→ I downloaded a PDF from Haute-Garonne’s government site, filled in the form and saved it on a USB key. Then I printed it at a Konica Minolta bizhub photocopier yesterday.