What's new?

Exponentials and logarithms – April 10, 2024.→ [preprint] ←
A narrative-style introduction to exponentials and logarithms… #math #reals #exponentiation
• September 10, 2024. Simplified the explanation of the intuition that lead to the definition of the logarithm as an integral. Correction of miscellaneous typos. The version of the preprint prior to this update can be found here. (see in page)

The Algebra Of Two’s Complements – May 14, 2024.→ [preprint] ←
Explaining the mathematics behind the standard way of representing negative numbers in binary. #binary-representation #twos-complements #modular-arithmetic
• August 13, 2024. Added a conclusion with a challenge for the reader, and changed the workflow of section 3, to start with the goal of having the most significant bit reserved for sign, and only then proceed to explain the need for modular arithmetic. Also did small improvements on the rest of the text. The version prior to this update can be retrieved here. (see in page)

Material Implication – June 22, 2024.→ [preprint] ←
A brief note explaining why the logical connective “implication” is defined the way it is. #implication #material-implication #logical-connective #induction #proof-by-contradiction
• August 2, 2024. Added a clarification explaining that we work in framework of classical logic. And improved the explanation for the “implication paradox” due to Gowers (note 4 in §2).

The Algebra Of Two’s Complements – May 14, 2024.→ [preprint] ←
Explaining the mathematics behind the standard way of representing negative numbers in binary. #binary-representation #twos-complements #modular-arithmetic
• May 26, 2024. Corrected typos and improved the explanation of when (and when not) does modular addition coincide with regular integer addition.

A revolução que falta – 25 de Abril de 2024. 🇵🇹
Cinquenta anos depois de Revolução dos Cravos, como ficou conhecida a mudança de regime operada a 25 de Abril de 1974, deixo aqui uma pequena reflexão, não tanto sobre o que foi conseguido—que é sobejamente conhecido, quer pelos apoiantes de Abril, quer pelos seus detractores—mas sobre aquilo que ficou a faltar. Algo que continua a causar muita confusão, mesmo entre as mais férreas hostes da revolução. #portugal #revolução #cravos #25abril

Enumerate: continuing from previous one – April 18, 2024.
How to have the bullet number continue from a previous enumeration. #latex #enumerate #bullet #number

Exponentials and logarithms – April 10, 2024.→ [preprint] ←
A narrative-style introduction to exponentials and logarithms… #math #reals #exponentiation

Exponentiation rules in $\mathbb{R}$ – March 22, 2024.[preprint]
This is something one usually learns in a piece-wise fashion, because it is information that is usually scattered among all sorts of different books (analysis, algebra, etc.). Well, here I round it all up in one place. #math #reals #exponentiation

Backup on LUKS-encrypted external HDD – March 8, 2022.[Script] [Config]
One of my strategies to prevent important (electronic-form) information from becoming too ephemeral… #backups #rsync #luks #usb #drive
• March 21, 2024. Script can now be used with a user-specified config file $ sh /path/to/backup_script.sh -f /path/to/custom/config/file.sh. I also added the ability to exclude certain files or folders from being backed up; cf. the new config template.

The revenge of rsync – March 19, 2024.
This is a repost of a text first published on June 2013, in my previous blog, erroneousthoughts.org (now decommissioned). It illustrates how just one tiny character, can make a world of difference… #rsync #source-folder #forward-slash

The dangers of abstraction – March 19, 2024.
This is a repost of a text first published on June 2013, in my previous blog, erroneousthoughts.org (now decommissioned). It offers a good illustration of what can lurk hidden under a software layer of abstraction… #rsync #sshfs #ssh

LaTeX: Restate theorems, etc. – June 26, 2023.
For when your mathematical creations need an alter ego… #latex #theorems #restate
• Update, December 10, 2023. Added a clarification about the need to actually repeat the content of the theorem or whatever, when restating it…

TeX-7 – November 20, 2023.[Source code]
This is my toned-down fork from Elias Toivanen’s TeX-9 Vim plugin for writing LaTeX documents. #vim #plugin #snippets
• Update, November 21, 2023. The plugin’s full manual is now displayed here. Within Vim, hitting :help vim-tex-seven will only list the available maps, visual mode motions, etc., together with brief descriptions of each—and direct the user to the current page for further information.

Backup on LUKS-encrypted external HDD – March 8, 2022.[Script] [Config]
One of my strategies to prevent important (electronic-form) information from becoming too ephemeral… #backups #rsync #luks #usb #drive
• Update, August 31, 2023. The script now outputs messages to inform the user when the LUKS volume has been successfully mounted/unmounted. Moreover, two new options: -m mounts the LUKS volume, and nothing else; and -u unmounts the LUKS volume, and nothing else. Also, the configuration variables have been placed in a separate file, to ease setting them up.