overlined

An overlined, or overbar, is a horizontal line placed above a symbol or expression. It is a versatile typographic convention used across disciplines to convey different meanings depending on context. In mathematics and related fields, the overline serves several common purposes.

In set theory and logic, Ā often denotes the complement of a set A within a universal set, meaning all elements not in A. In topology and analysis, the overline is used to indicate the closure of a set, written as Ā, which includes the limit points of the set. In statistics and data presentation, X̄ denotes the sample mean of a variable X.

In complex analysis and related areas, z̄ denotes the complex conjugate of a complex number z. This operation reflects a point across the real axis in the complex plane and has important algebraic properties. In physics, barred symbols label antiparticles, such as p̄ for an antiproton, and overlines are used in various quantum and particle-physics notations.

In computing and digital logic, an overline can be used informally to indicate negation or inversion of a signal or bit in some contexts, though more common actuarial or programming conventions use other symbols for NOT. In typography and linguistics, the overline is a general marking tool, and while a macron (a diacritic placed above vowels) is the standard mark for vowel length in many languages, an overline can appear in specific transcription schemes or stylistic typesetting.

Overall, the meaning of an overline is context-dependent, spanning complement, negation, mean, conjugation, and various stylistic or symbolic conventions.