# Differences

This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision | ||

relation_concatenation [2013/09/05 22:29] nikolaj |
relation_concatenation [2013/09/05 22:33] nikolaj |
||
---|---|---|---|

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]] |