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relation_concatenation [2013/08/06 20:59]
nikolaj
relation_concatenation [2013/09/05 22:33]
nikolaj
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 | @#88DDEE: $ S \in \text{Rel}(V,​Y) $ | | @#88DDEE: $ S \in \text{Rel}(V,​Y) $ |
  
-| @#55EE55: $ \langle x,y \rangle \in S\circ R $ |+| @#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  $ | | @#55EE55: $ \exists m.\ \langle x,m \rangle \in R \land \langle m,y \rangle \in S  $ |
  
-==== Ramifications ​==== +==== Discussion ​====
-=== Satisfies ​===+
 Concatenations/​compositions are associative. 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  A mayority of uses of the relation concatenation is when the relation is functional, i.e. one composes functions alla 
  
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 $(f\circ g)(x):​=f(g(x))$ $(f\circ g)(x):​=f(g(x))$
 +=== 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 ==== ==== Context ====
-Set constructor +=== Requirements ​===
-=== Parents ​===+
 [[Binary relation]] [[Binary relation]]
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