collection of sets indexed by set consisting of 5 members
- Thread starter Enh0702
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First, the question wants you to create an example. Thus, there is no one right answer; there are probably infinitely-many valid answers. You need to create one.
Second, how does your book define the "indexing" of a set?
Thank you!
Eliz.
Second, how does your book define the "indexing" of a set?
Thank you!
Eliz.
pka
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Here is one of an infinite collections of examples.
If \(\displaystyle A = \left\{ {1,2,3 \cdots ,98,99} \right\}\) is a set of the first 100 counting numbers, then let \(\displaystyle A_k = \left\{ {z \in A:\bmod (z,5) = k} \right\},\quad k = 0,1,2,3,4\). So each \(\displaystyle A_k\) is the set of numbers in A having remainder k when divided by 5.
Example: \(\displaystyle A_3 = \left\{ {3,8,13, \cdots ,93,98} \right\}\).
Now the collection \(\displaystyle \left\{ {A_k } \right\},\quad k = 0,1,2,3,4\) is an indexed family of sets.
If \(\displaystyle A = \left\{ {1,2,3 \cdots ,98,99} \right\}\) is a set of the first 100 counting numbers, then let \(\displaystyle A_k = \left\{ {z \in A:\bmod (z,5) = k} \right\},\quad k = 0,1,2,3,4\). So each \(\displaystyle A_k\) is the set of numbers in A having remainder k when divided by 5.
Example: \(\displaystyle A_3 = \left\{ {3,8,13, \cdots ,93,98} \right\}\).
Now the collection \(\displaystyle \left\{ {A_k } \right\},\quad k = 0,1,2,3,4\) is an indexed family of sets.