Variable (mathematics) - Notation

Notation

In mathematics, single-symbol names for variables are the norm. Following the 17th century French philosopher and mathematician, René Descartes, letters at the beginning of the alphabet, e.g. a, b, c are commonly used for constants and letters at the end of the alphabet, e.g. x, y, z, and t are commonly used for variables. In printed mathematics, variables and constants are usually set in an italic typeface.

Specific branches and applications of mathematics usually have specific naming conventions for variables. Variables with similar roles or meanings are often assigned consecutive letters. For example, the three axes in 3D coordinate space are conventionally called x, y, and z, while random variables in statistics are usually named X, Y, Z. In physics, the names of variables are largely determined by the physical quantity they describe, but various naming conventions exist.

A convention often followed in probability and statistics is to use X, Y, Z for the names of random variables, with these being replaced by x, y, z for observations or sample outcomes of those random variables. These latter (lower case) symbols are ordinary mathematical variables. The former (upper case) symbols actually stand for functions from the sample space (set of atomic outcomes) of the experiment to (typically) the real numbers. Another convention sometimes used in statistics is to denote population values of particular statistics by lower (or upper) case Greek letters, with sample-based estimates of those quantities being denoted by the corresponding lower (or upper) case letters from the ordinary alphabet.