Begincases

Begincases is a term used in mathematical writing to indicate the start of a case distinction or piecewise definition. It refers to the moment when a statement or function is defined by listing separate expressions according to different conditions.

In practice, begincases appears primarily in the context of LaTeX typesetting and mathematical templates. While there is no universal LaTeX command literally named “begincases” in the standard packages, many documents use a cases environment or a similarly labeled macro to present piecewise definitions. The phrase is often used informally to describe the logical beginning of the case list, which continues until the end of the case list.

A typical use-case is defining a function by cases. For example, a function f might be defined as f(x) = x^2 if x > 0, and f(x) = -x if x ≤ 0. In typeset form, this is presented as a piecewise expression with each branch accompanying a condition. Begincases emphasizes the legal boundary between the conditions and their corresponding expressions, helping readers distinguish the separate cases involved in the definition.

Variants of this approach appear across disciplines, including algebra, calculus, and computer science, wherever a single object is described by alternative expressions depending on context. Related concepts include piecewise functions, indicator functions, and the general technique of case analysis in proofs.

See also: piecewise function, cases environment, LaTeX typesetting, case analysis.