Indexed Family (mathematics)

Formally, a family is a triple (''X'', ''I'', ''ι'') of sets ''X'' and ''I'' and a Surjective Function ''ι'': ''I'' → ''X''. NOTATION A family is denoted by (''A''_''i'')_{''i''∈''I''} where ''I'' is the index set and ''i'' → ''A''_''i'' is the mapping. So ''A''_''i'' is the element belonging to the key ''i'' , also called the ''i''-th element of the family. Using curly brackets instead of parentheses, {''A''_''i''}_{''i''∈''I''} , indicates a Multiset (provided no element occurs more than a finite number of times).
	Like A	"http://wwwinformationdelightinfo/encyclopedia/entry/set" class="copylinks">Set , a family is a container and any set ''X'' gives rise to a family (''x'')<sub>''x''&isin''X''</sub> Thus any set naturally becomes a family For any family (''A''<sub>''i''</sub>)<sub>''i''&isin''I''</sub> there is the set of all elements {''A''<sub>''i''</sub> ''i''&isin''I''}, but this does not carry any information on multiple containment or the structure of ''I'' Hence, by using a set instead of the family, some information might be lost

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