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 relation_concatenation [2013/09/05 22:29]nikolaj relation_concatenation [2013/09/05 22:33]nikolaj 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 9: Line 9: ==== Discussion ==== ==== Discussion ==== - === Satisfies === Concatenations/​compositions are associative. Concatenations/​compositions are associative. - === 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 $|f(x)|$. + - === 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 Line 23: Line 20: $(f\circ g)(x):​=f(g(x))$ $(f\circ g)(x):​=f(g(x))$ + === 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]]