Can the statements be used interchangeably?
(1) The set-builder notation defines a set.
(2) The set-builder notation describes a set.
I'm really confused with these two words.
My understanding of the terminology is that (1) and (2) are both true, but (1) is stricter.
So, whenever we define a set, we also describe it. But whenever we describe a set, we don't necessarily define it.
So here's an example of a set description that is not a definition: A is a set with three elements.
Here is a definition of a set, which is also a description: Let A = {1,2,3}.