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Dharmasam Vardhini posted an Question
October 09, 2020 • 02:28 am
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Explain the rounded remark ( index set )
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Srinath Best Answer
An index set is a set, whose elements are used to 'index' or 'list' the elements of some other non empty set. Here, it is used to identify a 'list' of sets, ( family of sets). A simple example: Consider the open interval S1 = (0,1). S2 = (1,2) and Sn = ( n-1,n) Now these family of sets S = {Sn} can be indexed or listed by, I = {1,2,3,...} the set of all natural numbers. Which means, For i € I, Si € S.
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Sir here i denotes ??? i € I
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i is any element in I, which denotes the set of all natural numbers, in this example.
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ok sir
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Thank you so much
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Srinath![best-answer]()
It can also be considered as a one-one function from I to S.