The Denjoy–Luzin–Saks theorem is a significant result in the field of real analysis, particularly in the theory of functions and their integrability. The theorem deals with the conditions under which a measurable function can be approximated by simple functions.
The Quine–McCluskey algorithm is a method used for minimizing Boolean functions, which is particularly valuable in digital logic design and circuit simplification. It is an algorithmic approach that serves as a systematic way to find the minimal expression of a Boolean function represented in terms of its truth table or its minterms.
The De Sitter double star experiment is a thought experiment proposed by the Dutch astronomer Willem de Sitter in the early 20th century. It is intended to illustrate aspects of general relativity, particularly the effects of gravity on light and the concept of gravitational wave propagation. In this experiment, assume there are two massive bodies (the "double stars") orbiting around each other. According to general relativity, massive objects curve spacetime, affecting the paths of nearby light rays.
A group is said to be diagonalizable if it can be represented in a certain way with respect to its action on a vector space, particularly in the context of linear algebra. More specifically, in the context of linear representations, a group is diagonalizable when its representation can be expressed in a diagonal form. In this context, consider a group \( G \) acting on a vector space \( V \) over some field, typically the complex numbers.
As of my last update in October 2023, Dick Bond is an astrophysicist known for his contributions to the field of cosmology and astrophysics. He has been involved in research related to the cosmic microwave background radiation, galaxy formation, and structure in the universe. Bond has also worked on various projects and collaborations that enhance the understanding of the large-scale structure of the cosmos and the fundamental properties of dark matter and dark energy.
A digital line graph is a graphical representation of data that shows trends over time or sequences. It typically consists of points plotted on a coordinate system, connected by straight lines, to illustrate changes in values across a given period or across different categories. Digital line graphs are widely used in various fields such as finance, science, and statistics to visualize data trends, compare different sets of data, and make interpretations more accessible.
Diodorus Cronus was a prominent ancient Greek philosopher, typically associated with the Megarian school of philosophy. He lived around the 4th century BCE and is known primarily for his work in logic, particularly his contributions to the theories of modality and the nature of time. Diodorus is often remembered for his "master argument," which is a formal argument against the possibility of future contingents—that is, statements about future events that are not yet determined.
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