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Produced by Charles Wells   Revised 2015-08-20
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OTHER SYMBOLS USED IN MATH

Introduction

• This list includes only the major meanings of the most common symbols, according to my judgment.
• The list of mathematical symbols in Wikipedia includes many other symbols but does not include all, or even most of, the meanings of the symbols.
• Like many other parts of abstractmath.org, in depth lexicographical research is needed (anyone have ten million dollars?) See Remarks about usage.
• More information about mathematical symbols may be found in individual entries in Mathworld and in Wikipedia.

Accented characters

Mathematicians frequently use an accent to create a new variable from an old one. This is usually done to denote a mathematical object with some specific functional relationship with the old one.

• The most commonly used accents over the letter are arrow, bar, check, dot, hat and tilde.
• prime and star may be used after the letter as a superscript.
• slash may be used across a relational symbol.

All of the accents except arrow and slash (as far as I know) have more than one meaning. In the list below, I mention some common meanings, but mathematicians may and do define other meanings for the symbols.

Arrow

• Expressions such as $\vec{a}$, $\vec{m}$, $\vec{v}$, $\vec{x}$ usually denote vectors.
• A variant is $\overset{\scriptscriptstyle\rightharpoonup}{x}$. (The symbol above the $x$ is called a "harpoon").
• In print, vectors are usually printed in boldface, for example "$\textbf{x}$", but the arrow version is easier to use at the blackboard.
• In LaTeX, $\vec{x}$ is coded as "\vec{x}".
• The arrow is also used stand-alone in arrow notation.

Bar

• For a variable $x$, "$\bar{x}$" is pronounced "x bar".
• In probability and statistics, the bar may be used to denote the sample mean of a random variable.
• In many branches of math, the bar may be used to denote the closure (however it is defined) of a substructure of a mathematical structure.
• The bar is also used to denote the conjugate of a complex number.
• The typographical name of the symbol is macron.