LaTeX in the context of "Desktop publishing"

In predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"), read as "there exists", "there is at least one", or "for some". Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.

Quantification in general is covered in the article on quantification (logic). The existential quantifier is encoded as U+2203 ∃ THERE EXISTS in Unicode, and as \exists in LaTeX and related formula editors.

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.

For example, the physicist Albert Einstein's formula ${\displaystyle E=mc^{2}}$ is the quantitative representation in mathematical notation of mass–energy equivalence.

A semantics encoding is a translation between formal languages. For programmers, the most familiar form of encoding is the compilation of a programming language into machine code or byte-code. Conversion between document formats are also forms of encoding. Compilation of TeX or LaTeX documents to PostScript are also commonly encountered encoding processes. Some high-level preprocessors, such as OCaml's Camlp4, also involve encoding of a programming language into another.

Formally, an encoding of a language A into language B is a mapping of all terms of A into B. If there is a satisfactory encoding of A into B, B is considered at least as powerful (or at least as expressive) as A.

"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "absurdity", depending on context. It is used to represent:

• The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity" come from this context.)
• The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics
• The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence
• The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r₀,⊥)

In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, and the LaTeX symbol.

TeX (/tɛx/), stylized within the system as TeX, is a typesetting program which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978. The term now refers to the system of extensions – which includes software programs called TeX engines, sets of TeX macros, and packages which provide extra typesetting functionality – built around the original TeX language. TeX is a popular means of typesetting complex mathematical formulae; it has been noted as one of the most sophisticated digital typographical systems.

TeX is widely used in academia, especially in mathematics, computer science, economics, political science, engineering, linguistics, physics, statistics, and quantitative psychology. It has long since displaced Unix troff (the previously favored formatting system), in most Unix installations (although troff still remains as the default formatter of the UNIX documentation). It is also used for many other typesetting tasks, especially in the form of LaTeX, ConTeXt, and other macro packages.