We can group sets together into collections of sets. (As a rule, we don’t call these collections “sets of sets”, as that can lead to paradoxes!)
We can index these collections with the members of another set. The structure of this indexing set (finite, infinite, countable, uncountable…) imparts a structure onto the collection of sets being indexed.
Let be a set. Then for all , such that , we call an Indexed Collection of Sets. Note that does NOT have to be a countable set, nor does it need to be “ordered” in any way.
However, if these sets are ordered in some way, we may get the following special kinds of Indexed Collections.
If , then is a Finite Sequence of sets (because it is *sequentially* ordered).
If , the set of Natural Numbers, then is an Infinite Sequence of sets.
Now go lift something heavy,