Glossary of mathematical symbols

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.

The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sorts of mathematical objects. As the number of these sorts has remarkably increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. For having more symbols, other typefaces are also used, mainly boldface ${\displaystyle \mathbf {a,A,b,B} ,\ldots }$, script typeface ${\displaystyle {\mathcal {A,B}},\ldots }$ (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur ${\displaystyle {\mathfrak {a,A,b,B}},\ldots }$, and blackboard bold ${\displaystyle \mathbb {N,Z,Q,R,C,H,F} _{q}}$ (the other letters are rarely used in this face, or their use is unconventional).

The use of Latin and Greek letters as symbols for denoting mathematical objects is not described in this article. For such uses, see Variable (mathematics) and List of mathematical constants. However, some symbols that are described here have the same shape as the letter from which they are derived, such as ${\displaystyle \textstyle \prod {}}$ and ${\displaystyle \textstyle \sum {}}$.

These letters alone are not sufficient for the needs of mathematicians, and many other symbols are used. Some take their origin in punctuation marks and diacritics traditionally used in typography; others by deforming letter forms, as in the cases of ${\displaystyle \in }$ and ${\displaystyle \forall }$. Others, such as + and =, were specially designed for mathematics.