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Relation concatenation
Definition
| $ R \in \text{Rel}(X,U) $ |
| $ S \in \text{Rel}(V,Y) $ |
| $ \langle x,y \rangle \in S\circ R $ |
| $ \exists m.\ \langle x,m \rangle \in R \land \langle m,y \rangle \in S $ |
Ramifications
Satisfies
Concatenations/compositions are associative.
Discussion
A mayority of uses of the relation concatenation is when the relation is functional, i.e. one composes functions alla
$g:X\to Y,\ \ f:Y\to Z$
then
$f\circ g:X\to Z$
$(f\circ g)(x):=f(g(x))$
Context
Set constructor
Parents
