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relation_concatenation [2013/09/05 22:33]
relation_concatenation [2014/03/21 11:11]
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-===== Relation concatenation ===== 
-==== Definition ==== 
-| @#88DDEE: $ R \in \text{Rel}(X,​U) $ | 
-| @#88DDEE: $ S \in \text{Rel}(V,​Y) $ | 
-| @#FFBB00: $ \langle x,y \rangle \in S\circ R $ | 
-| @#55EE55: $ \exists m.\ \langle x,m \rangle \in R \land \langle m,y \rangle \in S  $ | 
-==== Discussion ==== 
-Concatenations/​compositions are associative. 
-A mayority of uses of the relation concatenation is when the relation is functional, i.e. one composes functions alla  
-$g:X\to Y,\ \ f:Y\to Z$ 
-$f\circ g:X\to Z$ 
-$(f\circ g)(x):​=f(g(x))$ 
-=== Notation === 
-If $f:X\to Y$ and $g:Y\to Z$ are functions, we'll often denote $f\circ g$ by $fg$. This convenient notation will also be used in more elaborate cases. For example, if by $f(x)$ we done the values of a function $f:​X\to\mathbb R$ and $|\cdot|$ is the function which takes a real to its absolute value, then $|f|$ will denote the name of the function with values $|f(x)|$. 
-==== Context ==== 
-Set constructor 
-=== Parents === 
-[[Binary relation]] 
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