# Composition

2010 Mathematics Subject Classification: *Primary:* 08A02 [MSN][ZBL]

A binary algebraic operation.

The composition (or superposition) of two functions $f:Y \rightarrow X$ and $g:Z \rightarrow Y$ is the function $h=f\circ g : Z \rightarrow X$, $h(z)=f(g(z))$.

The composition of two binary relations $R$, $S$ on set $A \times B$ and $B \times C$ is the relation $T = R \circ S$ on $A \times C$ defined by $a T c \Leftrightarrow \exists b \in B \,:\, a R b, b S c$.

See Convolution of functions concerning composition in probability theory.

See Automata, composition of concerning composition of automata.

See also: Composition (combinatorics), an expression of a natural numbers as an ordered sum of positive integers; Composition series, a maximal linearly ordered subset of a partially ordered set.

**How to Cite This Entry:**

Composition.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=41800