mathematical symbol

A mathematical symbol is a single character that carries a fixed meaning, so that you can write mathematics the way you write words. The plus sign + says “add,” the equals sign = says “is the same as,” and a letter like x says “some number.” Each symbol is a tiny package of meaning everyone agrees on.

Symbols come in kinds. Some are operations (+, −, ×, ÷) telling you what to do; some are relations (=, <, >, ≤, ≥) telling you how two quantities compare; some name objects (letters for variables, π and e for particular numbers); and some are grouping marks (parentheses, brackets) that say “handle this part as a unit.” Reading mathematics is largely a matter of knowing which kind of symbol you are looking at.

The meaning of a symbol is a convention, fixed by agreement rather than by nature, and it can shift with context. The cross × means multiply for numbers but cross product for vectors; a raised −1 can mean a reciprocal (x^−1) or an inverse function (f^−1); juxtaposition means multiply in algebra. Because symbols are shared agreements, the only firm rule is to use each in its standard sense and to state plainly when you mean something unusual.