Difference between revisions of "Composition"
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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 (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 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 | + | 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 $a T c \Leftrightarrow \exists b \in B \,:\, a R b, b S c$. |
See [[Convolution of functions]] concerning composition in probability theory. | See [[Convolution of functions]] concerning composition in probability theory. | ||
See [[Automata, composition of]] concerning composition of automata. | See [[Automata, composition of]] concerning composition of automata. | ||
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| + | 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. | ||
Latest revision as of 14:29, 3 September 2017
2020 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.
Composition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Composition&oldid=35691