Disjunction and existence are concepts that appear in mathematics, logic, and philosophy, often related to the interpretation of statements and claims. ### Disjunction **Definition**: In logic, a disjunction is a compound statement formed using the logical connective "or.

Indecomposability in the context of intuitionistic logic relates to the properties of certain types of propositions, specifically the way that statements can or cannot be decomposed into simpler parts. In intuitionistic logic, which is a form of logic that emphasizes constructivist principles and rejects the law of excluded middle (which states that any proposition is either true or false), indecomposability plays a crucial role in understanding the structure of proofs.

An **inhabited set** is a concept primarily used in type theory and computer science, particularly in the context of programming languages and type systems. A set is said to be inhabited if it contains at least one element.

Intuitionism is a philosophical approach primarily associated with mathematics and epistemology. It emphasizes the role of intuition in the understanding of mathematical truths and ethical values. There are two main contexts in which intuitionism is discussed: 1. **Mathematical Intuitionism**: This is a viewpoint established by mathematicians like L.E.J. Brouwer in the early 20th century. It posits that mathematical objects are constructed by the mind rather than discovered as pre-existing entities.

The Limited Principle of Omniscience is a concept primarily discussed in the realm of epistemology and philosophy of mathematics, particularly in connection with systems of logic and formal theories. The principle suggests that while an omniscient being would know all truths, certain formal systems (like those used in mathematics) can be seen as "limited" in their capacity for knowledge or truth affirmation.

Markov's principle is a concept in mathematical logic, particularly in the area of intuitionistic logic, which deals with the constructive aspects of proof and reasoning. It can be informally stated as follows: If it is provable that a certain property \( P(n) \) holds for some natural number \( n \), then there exists a specific natural number \( n_0 \) such that we can find a proof of \( P(n_0) \).

The modulus of continuity is a concept used in mathematical analysis to quantify how uniformly continuous a function is over a specific interval or domain.

As mentioned at youtu.be/16BzIG0lrEs?t=397 from Video "Applied Materials by Asianometry (2021)", originally the companies fabs would make their own equipment. But eventually things got so complicated that it became worth it for separate companies to focus on equipment, which then then sell to the fabs.

Non-constructive algorithm existence proofs refer to a type of proof that establishes the existence of a mathematical object or solution without providing a method for explicitly constructing it. In other words, these proofs show that at least one object with certain properties exists, but they do not give an algorithm or step-by-step procedure to find or build that object. ### Characteristics of Non-constructive Existence Proofs: 1. **Existential Quantification**: Non-constructive proofs often use existential quantifiers.

Realizability is a concept in mathematical logic and computer science that connects formal proofs with computational models. It primarily provides a way to interpret mathematical statements not just as abstract entities but also as constructive objects or processes. ### Key Aspects of Realizability: 1. **Formal Systems**: In the context of formal systems, realizability assigns computational content to formulas in logic. For example, a proof of a statement can be thought of as a program that "realizes" that statement.

Fluid mechanics is a branch of physics and engineering that studies the behavior of fluids (liquids and gases) in motion and at rest. It involves understanding how fluids interact with forces and with solid boundaries, how they flow, and how they respond to changes in pressure and temperature. Fluid mechanics is typically divided into two main areas: 1. **Fluid Statics**: This area focuses on fluids at rest.

Shock waves are a type of disturbance that moves faster than the local speed of sound in a medium. They can occur in various contexts, including physics, engineering, and even biology. Here are some key points about shock waves: ### Characteristics: 1. **Supersonic Speed**: Shock waves propagate at supersonic speeds, meaning they travel faster than the speed of sound in the medium through which they are moving.

Bending of plates refers to the deformation that occurs in thin, flat structures—often referred to as plates—when they are subjected to external loads, moments, or forces. This phenomenon is a crucial aspect of structural engineering and mechanical engineering, as it affects the performance and integrity of various structures, such as beams, bridges, and airplane wings. The bending of plates can be analyzed using different theories, depending on the thickness of the plate and the nature of the applied loads.