Indexed Families of Sets Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

The first hurdle I had to get past when I learned about indexed families of sets was simply how to read and use the notation that goes with them. This discussion is meant to help you over that same hurdle. Use the discussion to share your ideas and questions about the following….

Suppose A₁ = {1, 2, 3}, A₂ = {-3, -2, -1}, and A₃ = {-4, -2, 0, 2, 4}. How would you describe these three sets as an indexed family? What would the natural indexing set be? How would you use that indexing set to write the union or intersection of all three sets?

Do you think the family {A₁, A₂, A₃} described above has to be indexed by numbers? In other words, are there other equivalent families that use something else as indices? If so, give some examples. If not, explain why not.

Can you think of some reasonably “real world” examples of indexed families of sets? Describe some such examples, saying what the indexing set for each is and saying as precisely as you can how indices correspond to members of the family.