This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).
By Noam Chomsky.
A good summary table that opens up each category much more can be seen e.g. at the bottom of en.wikipedia.org/wiki/Automata_theory under the summary thingy at the bottom entitled "Automata theory: formal languages and formal grammars".
norm sequence convergence does not imply pointwise convergence by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This is related to the underlying SVG pain point of SVG background color:
Set of all decision problems solvable by a Turing machine, i.e. that decide if a string belongs to a recursive language.
To change font size: stackoverflow.com/questions/21363334/how-to-add-font-size-in-subtitles-in-ffmpeg-video-filterThe default appears to be 24, so just multiply that by whatever seems like a reasonable factor.
ffmpeg -i input.mp4 -vf "subtitles=subtitle.srt:force_style='Fontsize=64'" output.mp4Note howver that .ass subtitle files can contain style information, which ffmpeg respects. Aegisub can produce and preview such styles, making .ass one of the best options.
The following things come to mind when you look into research in this area, especially the search for BB(5) which was hard but doable:
- it is largely recreational mathematics, i.e. done by non-professionals, a bit like the aperiodic tiling. Humbly, they tend to call their results lemmas
- complex structure emerges from simple rules, leading to a complex classification with a few edge cases, much like the classification of finite simple groups
Bibliography:
Written in C#.
Turing machine acceleration refers to using high level understanding of specific properties of specific Turing machines to be able to simulate them much fatser than naively running the simulation as usual.
Acceleration allows one to use simulation to find infinite loops that might be very long, and would not be otherwise spotted without acceleration.
This is for example the case of www.sligocki.com/2023/03/13/skelet-1-infinite.html proof of Skelet machine #1.
First import video with:They don't have an
aegisub-3.2 ourbigbook-parent.mkvaegisub executable without the version number. Amazing.If you already have a subtitle file that you want to edit, then just pass it on as well:
aegisub-3.2 ourbigbook-parent.mkv ourbigbook-parent.assEnter: finish editing the current entry and start a new one.
This section is about the definition of the dot product over , which extends the definition of the dot product over .
Some motivation is discussed at: math.stackexchange.com/questions/2459814/what-is-the-dot-product-of-complex-vectors/4300169#4300169
Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.
Project trying to compute BB(5) once and for all. Notably it has better presentation and organization than any other previous effort, and appears to have grouped everyone who cares about the topic as of the early 2020s.
Very cool initiative!
By 2023, they had basically decided every machine: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. 
- Infinitely deep tables of contents:
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