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Difference between revisions of "Composition"

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A binary [[Algebraic operation|algebraic operation]]. For example, the composition (or superposition) of two functions $f$ and $g$ is the function $h=f\circ g$, $h(x)=f(g(x))$. See [[Convolution of functions|Convolution of functions]] concerning composition in probability theory.
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A binary [[Algebraic operation|algebraic operation]].  
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The composition (or superposition) of two functions $f:X \rightarrow Y$ and $g:Z \rightarrow Y$ is the function $h=f\circ g : Z \rightarrow X$, $h(z)=f(g(z))$.  
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The composition of two [[binary relation]]s $R$, $S$ on set $A \times B$ and $B \times C$ is the relation $T = R \circ S$ on $A \times C$ defined by $a T c \Leftrightarrow \exists b \in A \,:\, a R b, b S c$.
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See [[Convolution of functions]] concerning composition in probability theory.

Revision as of 20:13, 21 November 2014


2020 Mathematics Subject Classification: Primary: 08A02 [MSN][ZBL]

A binary algebraic operation.

The composition (or superposition) of two functions $f:X \rightarrow Y$ 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 $a T c \Leftrightarrow \exists b \in A \,:\, a R b, b S c$.

See Convolution of functions concerning composition in probability theory.

How to Cite This Entry:
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=34726
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