In my country, there's a long-standing tradition of using the vinculum in contexts similar to this:

Let $\overline{ab}$ be a two-digit natural number. Show that ...

I have only happened once to come across an explanation for this notation in a textbook. It stated that the "bar" (more technically, the vinculum) above a group of variables serves to distinguish digit representation of a number from multiplication $a\cdot b$.

However, I have never seen the vinculum being used in this way in English mathematics literature, its uses being restricted to:

  • part of the radical symbol $\surd$, e.g. $\sqrt{a^2+b^2}$
  • repeating decimals, e.g. $0.\overline{75}=0.757575\ldots$
  • complex conjugate, e.g. if $z=a+\text{i}b$, then $\overline{z}=a-\text{i}b$
  • negation of a logical expression, e.g. $\overline{A\lor B}$
  • line segment $\overline{AB}$ between points $A$ and $B$
  • fractions and division in general (seems dubious to me), e.g. $\dfrac{a}{b},\ \ \dfrac{7+5}{3+1}$

Has anyone else seen the vinculum being used for grouping the digits of a number? Perhaps the vinculum has other uses outside of English-speaking countries?

  • 1
    $\begingroup$ Perhaps the lack of finding this is related to the fact that for "real" math the digit representation is not of much concern; this is often more related to "recreational" math (e.g., magic tricks). In other words, have you found any English mathematics literature that uses the concept at all and introduces a different notation? $\endgroup$ – Hagen von Eitzen Jul 10 '15 at 9:20
  • $\begingroup$ I don't think this concept has to do anything with recreational maths. Suppose $a$ is the tens digit and $b$ is the ones digit. Then the number $ab$ can be written as $10a+b$. Using the notation with the vinculum the expression becomes $\overline{ab}=10a+b$. Employing the vinculum allows $a$ and $b$ to stand for two different things - both a digit and an unknown quantity. That's the notational difference I'm trying to figure out. $\endgroup$ – Rokas Jul 10 '15 at 9:37

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