In such situations, the elements of could be referenced by using the indexing set , such as for some . On the other hand, quite often, indexing sets are used without explicitly defining a surjective function. When this occurs, the elements of are referenced by using subscripts (also called indices) which are elements of , such as for some . If, however, the surjection from to were called , this notation would be quite to the function notation: .
Multiple indices are possible. For example, consider the set . Some people would consider the indexing set for to be . Others would consider the indexing set to be . (The double indices can be considered as ordered pairs.) Thus, in the case of multiple indices, it need not be the case that the underlying function be a surjection. On the other hand, must be a partial surjection. For example, if a set is indexed by , the following must hold:
For every , there exist and such that ;
For every , the map defined by is a partial function;
For every , the map defined by is a partial function.
|Date of creation||2013-03-22 16:07:51|
|Last modified on||2013-03-22 16:07:51|
|Last modified by||Wkbj79 (1863)|