A first-order predicate, also known as a first-order relation, is a fundamental concept in mathematical logic and predicate logic. It refers to a statement or a function that can take one or more arguments and returns a true or false value based on those arguments. ### Key Components of First-order Predicate Logic: 1. **Predicates**: A predicate is a function that takes one or more arguments and returns a truth value (true or false).
The concept of "first-move advantage" in chess refers to the inherent advantage that the player who moves first (White) has over the player who moves second (Black). This advantage stems from several factors: 1. **Initiative**: White can dictate the pace and flow of the game from the outset, allowing them to implement their strategy and pressure Black to respond.
A subsequential limit is a concept in real analysis and topology used to describe the behavior of a sequence of real numbers or points in a metric space.
A **permutable prime** (also known as a **chickens prime**) is a type of prime number that remains prime when its digits are permuted in any order. In other words, any rearrangement of the digits of a permutable prime must also be a prime number. For example, the number 197 is a permutable prime because: - 197 is prime, - 179 is prime (a permutation of the digits), - 791 is prime (another permutation).
A Tether Car is a small model car that is powered by a rubber band or a small engine and is tethered to a central point on a track via a long, flexible string or wire. As the car is released, it accelerates away from the tether point, often achieving high speeds. The design is usually lightweight to maximize performance, and the car's movement is constrained by the tether, which allows for controlled racing on a circular or oval track.
The term "Thai mathematicians" generally refers to mathematicians from Thailand or those who have studied or made significant contributions to mathematics in the context of Thailand. Thailand has a rich educational and cultural history, and its mathematicians have contributed to various fields, including pure and applied mathematics, statistics, and mathematical education. Some notable Thai mathematicians and scholars include: 1. **Prof. Dr. Ratanawadi G. Apinun** - Known for contributions in mathematics and mathematical education.
"Four fours" is a mathematical puzzle that involves using exactly four instances of the number four and various mathematical operations to create the numbers from 0 to 100. The challenge is to find expressions for each number using only four instances of the digit 4 and standard mathematical operations, such as addition, subtraction, multiplication, division, square roots, factorials, and concatenation.
In mathematics, particularly in the area of ring theory, the concept of a fixed-point subring can arise in various contexts. While the term "fixed-point subring" may not have a universally standardized definition, it can be understood in the framework of fixed points in algebraic structures. A fixed-point of a function is an element that is mapped to itself by that function.
Pessimistic induction is a philosophical argument primarily used in the philosophy of science to challenge the reliability of scientific theories. The core idea is that if we look at the history of science, we can see that many scientific theories that were once widely accepted have eventually been proven false. Based on this historical pattern, one might conclude that current scientific theories are also likely to be false or will eventually be overthrowed.
Flash spotting typically refers to the phenomenon of observing a brief, intense flash of light, often associated with natural occurrences like lightning or man-made sources like fireworks. In various contexts, "flash spotting" could be employed in different ways, such as: 1. **Astronomy**: Referring to spotting brief flashes from meteors entering the Earth's atmosphere, sometimes called "shooting stars.
Miller's theorem is a concept used in electrical engineering, particularly in the analysis of linear circuits with dependent sources. It provides a method for simplifying complex circuit configurations, particularly those involving voltage-controlled or current-controlled sources. ### Key Points of Miller's Theorem: 1. **Miller Effect**: It often deals with capacitors or resistances connected between the input and output of an amplifier or in a feedback loop.
Monster vertex algebra is a mathematical structure that arises in the context of conformal field theory, representation theory, and algebra. It is closely associated with the Monster group, which is the largest of the sporadic simple groups in group theory. The Monster vertex algebra is notable for its deep interconnections with various areas of mathematics, including number theory, combinatorics, and string theory.
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





