overlineA

Overline A, written as Ā or \overline{A}, is a notation used in various branches of mathematics and logic to indicate a derived or related object to A. The exact meaning depends on the mathematical framework and the conventions of the text.

In set theory and logic, Ā commonly denotes the complement of A with respect to a universal set U, meaning Ā = U \ A. In Boolean algebra and propositional logic, Ā is often used to represent NOT A. The complement interpretation requires a clearly specified universal set to avoid ambiguity.

In topology, Ā can denote the closure of A, which is the smallest closed set containing A. The closure includes A itself and all limit points of A, providing a way to “complete” A within a given space.

In complex analysis and related fields, Ā is frequently used for the complex conjugate of a complex number A, when A is complex-valued. For a complex number z = x + yi, the conjugate is z̄ = x − yi. The conjugate operation preserves many algebraic properties while reversing the sign of the imaginary part.

Because Ā can signify different concepts in different contexts, readers should rely on the surrounding definitions to determine its meaning in a given text. In typesetting, Ā is produced in LaTeX with \overline{A}, yielding a horizontal bar over the letter A.