Probability fallacies are misconceptions or errors in reasoning related to probabilities, often leading individuals to draw incorrect conclusions based on how they interpret statistical information or probability outcomes. These fallacies stem from human intuition and cognitive biases, which can distort understanding of probability and risk. Here are some common examples of probability fallacies: 1. **Gambler's Fallacy**: This fallacy involves the belief that past independent events affect the likelihood of future independent events.
Formal systems are structured frameworks used in mathematics, logic, computer science, and other fields to rigorously define and manipulate symbols and statements according to a set of rules. Here are the main components of a formal system: 1. **Alphabet**: This consists of a finite set of symbols used to construct expressions or statements in the system. 2. **Syntax**: Syntax defines the rules for constructing valid expressions or statements from the symbols in the alphabet.
Independence results can refer to various concepts depending on the context in which the term is used. Here are a few interpretations: 1. **Mathematics and Logic**: In mathematical logic, particularly in set theory and model theory, independence results refer to propositions or statements that can be proven to be independent of a given axiomatic system.
Large-scale mathematical formalization projects refer to extensive efforts aimed at translating mathematical concepts, theorems, and proofs into formal languages that can be processed by computers. These projects typically involve the use of formal proof assistants or theorem provers, which are software tools that help users construct mathematical proofs in a precise and verifiable manner.
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!
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