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No open signup it seems. TODO CV of owner.
They are making a proof assistant to integrate into the website: github.com/bookofproofs/fpl/, reminds Ciro Santilli of website front-end for a mathematical formal proof system.
Ciro Santilli appreciates this concept of "remembering the suffering of others" a lot due to Ciro Santilli's self perceived compassionate personality and Ciro Santilli's cheapness.
A good definition is by using Dedekind cuts.
This is the possibly infinite dimensional version of a Hermitian matrix, since linear operators are the possibly infinite dimensional version of matrices.
There's a catch though: now we don't have explicit matrix indices here however in general, the generalized definition is shown at: en.wikipedia.org/w/index.php?title=Hermitian_adjoint&oldid=1032475701#Definition_for_bounded_operators_between_Hilbert_spaces
Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.
The literal Chinese name says it all: "Fake Mountain". The stones evoke the feeling of the beautiful rock mountains of China.
The term "奇石假山" (qi2 shi2 jia3 shan1, lit. "weird shaped stone fake mountain") is also used, almost as a synonym by many people, since the stones are often chose in interesting shapes. Choosing the right stone is basically an art form in itself.
The stones used are generally limestone, which as a sedimentary rock is weaker, and more likely to be eroded into interesting shapes.
Tinker Tailor Soldier Spy adaptation by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.
But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.
One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.
Elements of a Lie algebra can (should!) be seen a continuous analogue to the generating set of a group in finite groups.
For continuous groups however, we can't have a finite generating set in the strict sense, as a finite set won't ever cover every possible point.
But the generator of a Lie algebra can be finite.
And just like in finite groups, where you can specify the full group by specifying only the relationships between generating elements, in the Lie algebra you can almost specify the full group by specifying the relationships between the elements of a generator of the Lie algebra.
This "specification of a relation" is done by defining the Lie bracket.
The reason why the algebra works out well for continuous stuff is that by definition an algebra over a field is a vector space with some extra structure, and we know very well how to make infinitesimal elements in a vector space: just multiply its vectors by a constant that cana be arbitrarily small.
That's what usually fucks up parallel programs.
Written mostly by Eric W. Weisstein.
Ciro once saw a printed version of the CRC "concise" encyclopedia of mathematics. It is about 12 cm thick. Imagine if it wasn't concise!!!
Infinite Napkin is the one-person open source replacemente we needed for it! And OurBigBook.com will be the final multi-person replacement.
Dual vectors are the members of a dual space.
In the context of tensors , we use raised indices to refer to members of the dual basis vs the underlying basis:The dual basis vectors are defined to "pick the corresponding coordinate" out of elements of V. E.g.:By expanding into the basis, we can put this more succinctly with the Kronecker delta as:
Note that in Einstein notation, the components of a dual vector have lower indices. This works well with the upper case indices of the dual vectors, allowing us to write a dual vector as:
In the context of quantum mechanics, the bra notation is also used for dual vectors.
Pinned article: ourbigbook/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:
- 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/derivative - 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 4. Visual Studio Code extension tree navigation.
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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant 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