An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a vinculum, a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign. The original use in Ancient Greek was to indicate compositions of Greek letters as Greek numerals. In Latin, it indicates Roman numerals multiplied by a thousand and it forms medieval abbreviations (sigla). Marking one or more words with a continuous line above the characters is sometimes called overstriking, though overstriking generally refers to printing one character on top of an already-printed character. An overline, that is, a single line above a chunk of text, should not be confused with the macron, a diacritical mark placed above (or sometimes below) individual letters. The macron is narrower than the character box.
Uses
Medicine
In most forms of Latin scribal abbreviation, an overline or macron indicates omitted letters similar to use of apostrophes in English contractions. Letters with macrons or overlines continue to be used in medical abbreviations in various European languages, particularly for prescriptions. Common examples include
a, a̅, or ā for ante ("before") c, c̅, or c̄ for cum ("with") p, p̅, or p̄ for post ("after") q, q̅, or q̄ for quisque and its inflections ("every", "each") s, s̅, or s̄ for sine ("without") x, x̅, or x̄ for exceptus and its inflections ("except") Note, however, that abbreviations involving the letter h take their macron halfway up the ascending line rather than at the normal height for Unicode overlines and macrons: ħ. This is separately encoded in Unicode with the symbols using bar diacritics and appears shorter than other overlines in many fonts.
Math and science
Decimal separator
In the Middle Ages, from the original Indian decimal writing, before printing, an overline over the units digit was used to separate the integral part of a number from its fractional part, as in 9995 (meaning 99.95 in decimal point format). A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal separator, as in 9995.
Vinculum In mathematics, an overline can be used as a vinculum. The vinculum can indicate a line segment: A B ¯ {\displaystyle {\overline {\rm {AB}}}} The vinculum can indicate a repeating decimal value: 1 7 = 0. 142857 ¯ = 0.142857142857142857142857... {\displaystyle {1 \over 7}=0.{\overline {142857}}=0.142857142857142857142857...} When it is not possible to format the number so that the overline is over the digit(s) that repeat, one overline character is placed to the left of the digit(s) that repeat: 3. I ¯ 3 = 3. 3 ¯ = 3.3333333333333333333333333... {\displaystyle 3.{\overline {\phantom {I}}}3=3.{\overline {3}}=3.3333333333333333333333333...}
3.12 I ¯ 34 = 3.12 34 ¯ = 3.123434343434343434343434... {\displaystyle 3.12{\overline {\phantom {I}}}34=3.12{\overline {34}}=3.123434343434343434343434...}
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:
x ¯ {\displaystyle {\overline {x}}} is the average value of x i {\displaystyle x_{i}}
Survival functions or complementary cumulative distribution functions are often denoted by placing an overline over the symbol for the cumulative: F ¯ ( x ) = 1 − F ( x ) {\displaystyle {\overline {F}}(x)=1-F(x)} .
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:
A ∪ B ¯ ≡ A ¯ ∩ B ¯ A ∩ B ¯ ≡ A ¯ ∪ B ¯ {\displaystyle {\begin{aligned}{\overline {A\cup B}}&\equiv {\overline {A}}\cap {\overline {B}}\\{\overline {A\cap B}}&\equiv {\overline {A}}\cup {\overline {B}}\end{aligned}}}
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