Free Boolean algebra is a concept in the field of abstract algebra that deals with Boolean algebras without imposing specific relations among the elements. In essence, a free Boolean algebra is generated by a set of elements (often called generators) without any relations other than those that are inherent to the properties of Boolean algebras. ### Key Characteristics of Free Boolean Algebras: 1. **Generators**: A free Boolean algebra is determined by a set of generators.
A Boolean domain refers to a logical system that operates on values that can be either true or false. The term often comes up in discussions related to Boolean algebra, which is a mathematical structure dealing with binary variables and their operations. In the context of computer science, the Boolean domain typically encompasses: 1. **Boolean Values**: The primary values in this domain are `true` and `false`.
A Boolean expression is a mathematical expression that evaluates to either true or false. It is formed using Boolean variables (which take on values of true or false) and logical operators, such as AND, OR, and NOT. The expression can be in the form of simple propositions or complex combinations. Here are some common logical operators: 1. **AND (∧)**: The result is true if both operands are true.
In mathematics, particularly in the field of order theory and lattice theory, a **division lattice** is a specific type of lattice structure that is primarily concerned with the division operation among its elements.
A **product term** is a concept used primarily in Boolean algebra and digital logic design. It refers to an expression formed by the logical AND (conjunction) of one or more variables or literals. In Boolean terms, a product term is characterized by the following features: 1. **Variables and their Complements**: Each variable can appear in its original form or as its complement.
A "Line House" typically refers to a type of residential building that is part of a row of connected houses, often sharing walls with adjacent properties. This architectural style is common in urban environments where space is limited. In some contexts, "line house" may refer to a very specific design or cultural interpretation of row houses, often characterized by their long, narrow structures. They can be found in various forms across different countries, each having its unique design features based on local building practices and climates.
Vera Šnajder appears to be a relatively lesser-known figure, as there is limited publicly available information about her. If you have a specific context in which you encountered her name—such as in literature, art, academia, or another field—I can help you more effectively.
Relation algebra is a formal system used to describe and manipulate relations, which are fundamental concepts in the fields of mathematics and computer science, particularly in databases. It provides a set of operations and algebraic laws that can be applied to relations, allowing for the querying and transformation of sets of data. ### Key Components of Relation Algebra: 1. **Relations**: A relation can be thought of as a table with rows and columns, where each row represents a tuple and each column corresponds to an attribute.
Liminal deities are deities or divine figures that exist at the boundaries or thresholds between different realms, states, or categories. The term "liminal" comes from the Latin word "limen," meaning "threshold." In various mythologies and belief systems, these deities often embody transitional states or play roles that connect contrasting domains, such as life and death, human and divine, or nature and culture.
Borders of administrative divisions refer to the boundaries that define the limits and extents of different administrative areas within a larger geographic entity, such as a country or region. These divisions can include various levels of governance, such as: 1. **Countries**: The most significant administrative division on a global scale. 2. **States or Provinces**: Subdivisions within a country, often having their own government.
The borders of the European Union (EU) refer to the external boundaries that demarcate EU member states from non-member states. These borders are significant because they not only define the geographical limits of the EU but also govern various legal and regulatory frameworks related to trade, immigration, and customs. Here are some key points to understand about the borders of the EU: 1. **Member States**: As of October 2023, the European Union consists of 27 member countries.
The **Natural Prolongation Principle** is a concept used primarily in the field of geology and geophysics, particularly in the context of understanding the behavior of geological formations and their resources, such as minerals or oil and gas. In essence, the principle suggests that geological features, like layers of rock or formations that contain resources, can be expected to continue in a natural and logical manner beyond their observed boundaries.
Cross-border public transport refers to the transportation services that operate across national borders, facilitating the movement of passengers between different countries. This can include various modes of transport, such as buses, trains, ferries, and even air travel, that link cities and regions in neighboring countries. Key features of cross-border public transport include: 1. **International Connectivity**: These services connect urban and rural areas in one country to those in another, enhancing regional integration and accessibility.
Cross-border rapid transit refers to transportation systems or services that facilitate quick and efficient movement of passengers or goods across national borders. These systems often utilize high-capacity transit modes, such as railways, buses, or dedicated transport corridors, designed to streamline the border crossing experience. Key features of cross-border rapid transit may include: 1. **Dedicated Infrastructure**: Specialized routes or lanes are designed to accommodate rapid transit vehicles, often bypassing congestion that typically occurs at border crossings.
Wikipedia categories named after borders typically refer to groups of articles that are classified based on the geographical or political boundaries between different regions, countries, or territories. These categories often include information about: 1. **Country Borders**: Categories might include articles on the borders shared between different nations, such as "Borders of Canada" or "Borders of Mexico." 2. **Political Divisions**: Some categories focus on internal borders within countries, like state borders in the United States or provincial borders in Canada.
The term "border town" typically refers to a town or city that is located near a border between two countries. These towns often serve as points of entry and exit for people and goods, and they can have unique cultural and social dynamics due to the proximity to another country. Border towns may have features such as customs checkpoints, trade markets, and diverse populations that reflect influences from both sides of the border. They can be significant for trade, tourism, and sometimes even for geopolitical issues.
The Demarcation Line, or "La Ligne de Démarcation," refers to the dividing line established during World War II in France following the country's defeat by Nazi Germany in 1940. After the armistice signed on June 22, 1940, France was split into two zones: 1. **Occupied Zone**: The northern and western parts of France were directly occupied by German forces.
Limes Saxoniae, also known as the Saxon Limes, refers to a historical boundary or defense system that marked the northern frontier of the Roman Empire in Germania, particularly in the region corresponding to modern-day Saxony in Germany. It represents a part of the larger network of Roman frontiers known as the "limes," which safeguarded the Roman Empire from external threats and marked the limits of Roman territorial control.
The term "green border" can refer to various concepts depending on the context. Here are a few interpretations: 1. **Environmental Context**: In environmental discussions, "green border" might refer to boundaries defined by natural landscapes, such as forests, parks, or other green spaces that provide ecological benefits, help in conserving biodiversity, or facilitate wildlife corridors.
In computing, the term "zombie" can refer to several different concepts, depending on the context. Here are the most common uses of the term: 1. **Zombie Processes**: In the context of operating systems, a zombie process (or defunct process) is a process that has completed its execution but still has an entry in the process table.

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!
We have two killer features:
  1. 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-calculus
    Articles 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
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant 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