Collection:
Term for the things that may somehow be
collected. The terms "set" and
"class" are often offered as synonyms, but there are good reasons to
keep these three terms apart, and use them according to the following
assumptions, as is done in this
Dictionary: Every set is a
class, every
set and every class is a collection, but there may be collections that
are not classes nor sets, and there may be classes that are not sets.
One example of such a class that is not a set is a
proper class. And one example of a
collection that seems neither a class nor a set is the collection
of all classes and all sets, including such as are not elements of
themselves. See: Russell's Paradox.
Note that the sense of "collected" is wide: Whether by physical means
or only by means of thought, imaginatively. Thus, there are, it would
seem, for a given large enough set, subsets
of the set that may be thought of somehow, if only by noting that all
the elements of the subset are elements of the set, but that subset need not in
any way be physically collected or even physically collectable.
Presumably, you never before thought of the set of {the oldest living
platypus, your grandmother, the Pope}, but even so it is a subset of the
set of things in this world, which is a set you spend considerable
thought about  and that the subset mentioned is such a subset I
have just pointed out to you.
