We work with sets in Hierarchy. A Group is a set. A set is a collection of elements and these can be anything. There are no restrictions–until we get to “ZF” Set Theory.
It is typical for a set to group together things that have a reason to be grouped together:
- Colors = {red, orange, yellow, green, blue, purple, brown, black}
- Mathematical Objects = {Geometric Spaces, Algebraic Structures}
The words “set” and “element” are called primitive notions, because we can’t define them in terms of anything else.
There might be some confusion because we actually did define a set as being a collection, but there is nothing technical about the noun “collection”, we found it convenient to use it in an informal discussion.
Appendix A
We’ve seen one reference define “;” as the Classifier. We hesitate to put this in our lexicon if we only find it in one reference.
An example of its use is shown below where we are defining the null set, 
The idea in the above definition is that it isn’t possible for there to exist an x that isn’t equal to itself, therefore, there will be nothing the set if we give the set this weird definition.
Rob Sterling 