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Ciro Santilli is a big believer that there is value in tutorials written by beginners, because beginners are more likely to explain things in a way that other beginners can understand.
Even though they make more mistakes, this more approachable point of view can be very valuable.
And mistakes/omissions can be corrected on comments by people with more knowledge, so that the writer also ends up learning something new.
By other people:
- jakobschwichtenberg.com/about/ from Jakob Schwichtenberg mentions quotes C. S. Lewis book "Reflections on the Psalms"[ref]:
It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. [...] The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago he has forgotten. He sees the whole subject, by now, in a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren't.
Cirocoins can only be issued by Ciro Santilli.
Cirocoins are strictly nominal, and cannot be traded by recipients with anyone but Ciro, i.e. they are extremely illiquid.
Cirocoins can be removed from recipients at any point if they commit non-Cirist acts.
It is not possible to give a precise number to how many Cirocoins anyone owns. This is decided on a transaction by transaction basis. Ciro can therefore only inform you if your Cirocoin balance increased or decreased, but any attached number has no value, and thus are equivalent to expressions of type "you gained/lost a Cirocoin".
Notable lists:
The reason why the epsilon delta definition is so venerated is that it fits directly into well known methods of the formalization of mathematics, making the notion completely precise.
Main motivation: Lebesgue integral.
The Bright Side Of Mathematics 2019 playlist: www.youtube.com/watch?v=xZ69KEg7ccU&list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Approximates an original function by sines. If the function is "well behaved enough", the approximation is to arbitrary precision.
Fourier's original motivation, and a key application, is solving partial differential equations with the Fourier series.
Can only be used to approximate for periodic functions (obviously from its definition!). The Fourier transform however overcomes that restriction:
The Fourier series behaves really nicely in , where it always exists and converges pointwise to the function: Carleson's theorem.
Just by havin the notion of neighbourhood, concepts such as limit and continuity can be defined without the need to specify a precise numerical value to the distance between two points with a metric.
As an example. consider the orthogonal group, which is also naturally a topological space. That group does not usually have a notion of distance defined for it by default. However, we can still talk about certain properties of it, e.g. that the orthogonal group is compact, and that the orthogonal group has two connected components.
Generalize function to allow adding some useful things which people wanted to be classical functions but which are not,
It therefore requires you to redefine and reprove all of calculus.
For this reason, most people are tempted to assume that all the hand wavy intuitive arguments undergrad teachers give are true and just move on with life. And they generally are.
One notable example where distributions pop up are the eigenvectors of the position operator in quantum mechanics, which are given by Dirac delta functions, which is most commonly rigorously defined in terms of distribution.
Distributions are also defined in a way that allows you to do calculus on them. Notably, you can define a derivative, and the derivative of the Heaviside step function is the Dirac delta function.
Key for quantum mechanics, see: mathematical formulation of quantum mechanics, the most important example by far being .
Collections and overviews:
- asciiart.website/index.php?art=people/naked%20ladies "Naked Ladies - Nude Women" category
- if you value medium over content, Ciro found two of the images reproduced in
asciiart.websiteabove also reproduced in the Bitcoin blockchain as described at: ASCII art, that should definitely turn you on, horny nerd
- if you value medium over content, Ciro found two of the images reproduced in
- www.reddit.com/r/ASCII_porn/ on Reddit boring
- www.vice.com/en/article/nepapk/ascii-pr0n-porn-predates-the-internet-but-its-still-everywhere-rule-34 ASCII Porn Predates the Internet But It's Still Everywhere by Vice News (2019)
You just couldn't resist Googling it and clicking this page, could you? You naughty, naughty bearded programmer nerd. Yes, I'm talking to you.
TODO it is quite hard to actually find non-automatically generated ASCII art of people fucking, most of them are just sexy/horny women drawn by bearded nerds, likely and based on sticky physical paper porn magazines from the 80's, good old days.
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/\Code 1. This image depicts the Chinese government fucking 1 million Chinese people in the ass during the Tiananmen Square Protests, which was undoubtedly one of the largest gang bangs of the late 20th century:
The IBM 1401 mainframe runs "Edith" by CuriousMarc
. Source. 1960's punched card ASCII porn. Vintage. EDITH is also mentioned e.g. at: www.threedee.com/jcm/aaa/index.html. No ASCII uploads found however: www.reddit.com/r/programming/comments/a2pser/the_ibm_1401_mainframe_runs_edith/.OMG, Ciro Santilli only learned about this in 2021 after: twitter.com/ryancdotorg/status/1375484757916672000
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- 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