repeat, one overline character is placed to the left of the digit(s) that repeat: Historically, the vinculum was used to group together symbols so that they could be treated as a unit. Today, parentheses are more commonly used for this purpose. Statistics The overline is used to indicate a sample mean: is the average value of Survival functions or complementary cumulative distribution functions are often denoted by placing an overline over the symbol for the cumulative: . Negation In set theory and some electrical engineering contexts, negation operators (also known as complement) can be written as an overline above the term or expression to be negated. For example: Common set theory notation: Electrical engineering notation: in which the times (cross) means multiplication, the dot means logical AND, and the plus sign means logical OR. Both illustrate De Morgan's laws and its mnemonic, "break the line, change the sign". Negative In common logarithms, a bar over the characteristic indicates that it is negative—whilst the mantissa remains positive. This notation avoids the need for separate tables to convert positive and negative logarithms back to their original numbers. Complex numbers The overline notation can indicate a complex conjugate and analogous operations. if , then Vector In physics, an overline sometimes indicates a vector, although boldface and arrows are also commonly used: Congruence classes Congruence modulo is an equivalence relation, and the equivalence class of the integer , denoted by , is the set }. This set, consisting of all the integers congruent to modulo , is called the congruence class, residue class, or simply residue of the integer modulo . When the modulus is known from the context, that residue may also be denoted or . Topological closure In topology, the closure of a subset S of a topological space is often denoted or . Improper rotation In crystallography, an overline indicates an improper rotation or a negative number: is the Hermann–Mauguin notation for a threefold rotoinversion, used in crystallography. is the direction with Miller indices , , . Maximal conductance In computational neuroscience, an overline is used to indicate the "maximal" conductances in Hodgkin-Huxley models. This goes back to at least the landmark paper published by Nobel prize winners Alan Lloyd Hodgkin and Andrew Fielding Huxley around 1952. Antiparticles Overlines are used in subatomic particle physics to denote antiparticles for some particles (with the alternate being distinguishing based on electric charge). For