# Differences

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 relation_concatenation [2013/09/05 22:33]nikolaj relation_concatenation [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/05 22:33 nikolaj 2013/09/05 22:33 nikolaj 2013/09/05 22:29 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:57 nikolaj 2013/08/06 20:57 nikolaj 2013/08/06 20:52 nikolaj 2013/08/06 20:52 nikolaj 2013/05/23 16:07 nikolaj 2013/05/23 15:21 nikolaj 2013/05/23 15:15 nikolaj 2013/05/18 18:00 nikolaj 2013/05/18 12:56 external edit2013/05/15 20:42 nikolaj 2013/05/15 20:22 nikolaj 2013/05/15 20:22 nikolaj created Next revision Previous revision 2013/09/05 22:33 nikolaj 2013/09/05 22:33 nikolaj 2013/09/05 22:29 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:59 nikolaj 2013/08/06 20:57 nikolaj 2013/08/06 20:57 nikolaj 2013/08/06 20:52 nikolaj 2013/08/06 20:52 nikolaj 2013/05/23 16:07 nikolaj 2013/05/23 15:21 nikolaj 2013/05/23 15:15 nikolaj 2013/05/18 18:00 nikolaj 2013/05/18 12:56 external edit2013/05/15 20:42 nikolaj 2013/05/15 20:22 nikolaj 2013/05/15 20:22 nikolaj created Line 1: Line 1: ===== Relation concatenation ===== ===== Relation concatenation ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $R \in \text{Rel}(X,​U)$ | + | @#55CCEE: context ​    | @#55CCEE: $R \in \text{Rel}(X,​U)$ | - | @#88DDEE: $S \in \text{Rel}(V,​Y)$ | + | @#55CCEE: context ​    | @#55CCEE: $S \in \text{Rel}(V,​Y)$ | - | @#FFBB00: $\langle x,y \rangle \in S\circ R$ | + | @#FFBB00: definiendum ​| @#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: postulate ​  | @#55EE55: $\exists m.\ \langle x,m \rangle \in R \land \langle m,y \rangle \in S$ | ==== Discussion ==== ==== Discussion ==== Line 22: Line 22: === Notation === === 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 $|f(x)|$. 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 ​==== + ==== Parents ​==== - Set constructor + === Context ​=== - === Parents ​=== + [[Binary relation]] [[Binary relation]]