A one-sided limit refers to the value that a function approaches as the input approaches a particular point from one side, either the left or the right. There are two types of one-sided limits: 1. **Left-Hand Limit**: This is denoted as \( \lim_{x \to c^-} f(x) \) and represents the value that \( f(x) \) approaches as \( x \) approaches \( c \) from the left (i.e.
Sean M. Carroll by Ciro Santilli 40 Updated 2025-07-16
Works at Caltech as of 2020.
But as usual, it falls too close to popular science for Ciro's taste.
AI safety by Ciro Santilli 40 Updated 2025-07-16
Basically ensuring that good AI alignment allows us to survive the singularity.
The PC-1, or PC-1 computer, refers to a specific model of personal computer that was introduced by various manufacturers during the early evolution of personal computing. However, the term "PC-1" isn't as commonly recognized as others, such as the IBM PC or Apple's early offerings. The most widely known "PC" refers to IBM's Personal Computer, which debuted in 1981 and set the standard for compatible personal computers.
Stephen Hawking by Ciro Santilli 40 Updated 2025-07-16
While learning black-hole stuff is not on top of Ciro Santilli's priorities, Hawking's spirit is to be admired.
To never give up even when everything seems lost, and still have a sense of humour is respectable.
An ex-physicist colleague who had met Hawking told an anecdote. Hawking was around in the department one day, they said hi and all. But then Hawking wanted to tell a joke. It took like 5 minutes of typing, and you can imagine that things were pretty awkward and the joke's timing was "a bit off". But Hawking did tell the joke nonetheless.
This is also suggested in the The Theory of Everything (2014) film, and therefore likely the biographies.
Sylvain Poirier by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli feels a bit like this guy:
singlesunion.org/ so cute, he's looking for true love!!! This is something Ciro often thinks about: why it is so difficult to find love without looking people in the eye. The same applies to jobs to some extent. He has an Incel wiki page: incels.wiki/w/Sylvain_Poirier :-)
Figure 1.
Sylvain's photo from his homepage.
Source. He's not ugly at all! Just a regular good looking French dude.
Video 1.
Why learn Physics by yourself by Sylvain Poirier (2013)
Source.
settheory.net by Ciro Santilli 40 Updated 2025-07-16
Notably, given the domain name, it is clear that he likes formalization of mathematics-stuff, like Ciro Santilli.
At first glance, looks a bit dry though, not many examples.
William Shockley by Ciro Santilli 40 Updated 2025-07-16
This dude is the charicature of the evil scientist! It is so funny. Brilliant, ambitious and petty!
The most important ones are:
Other super important ones:
This is perhaps slightly worse than the Tinker Tailor Soldier Spy, but still amazing.
Some difficult points:
  • how did the general deduce that the old woman's daughter had a link to Karla? It must be linked to the fact that the Russian agent who made the offer was a Karla-man.
  • some things are hard to understand without having seen the previous Tinker Tailor Soldier Spy, e.g. they say nothing clearly who Toby Esterhase is, he now works on art sales
  • but others are inconsistent, e.g. they changed the actor for Peter Guillam...
Video 1.
Smiley's letter to Karla scene from Smiley's People 1982 BBC miniseries John le Carré adaptation EP6o
. Source. Fan-uplod by Ciro Santilli, one of the greatest television scenes ever. Blocked in the UK.
Looking Glass Universe by Ciro Santilli 40 Updated 2025-07-16
Cute simple paper-cut stop motion animations videos by Mithuna Yoganathan, a PhD in theoretical physics at the University of Cambridge: www.damtp.cam.ac.uk/person/my332.
This has the seeds of direct good intuition, but often stops a bit too short. Worth a look though, there is value in them for beginners.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact