We define the term "Set" as,
A set is a collection of objects.
And an "Empty set" as,
An empty set is a set which contains nothing.
First problem I encountered:
How the definition of "Empty set" is consistent with the definition of "sets" if "Empty set" contains nothing and a "set" is a collection of objects.
Further we discovered in set theory that every set has a subset that is the Null set.
Such as,
If $A=\emptyset$ and $B=\{1,2,3\}$ then,
$$A \subset B$$
Second problem I encountered:
How and why "No element" is referred and considered as an element as we do in case of null set that is, when we say that every set has a subset that is the Null set?
Third and Last one:
How can a set possess "some thing" and "nothing" simultaneously that is when we say that every set (containing objects) has a subset which is Null set (contains nothing)?
Best Answer
A shopping bag is an object to carry things; an empty bag is a bag with nothing inside it.
From the viewpoint of people trained in mathematics, the explanation "a set is a collection of objects" is formally consistent with the set being empty (in which case the set is a collection of no objects).
But perhaps, at first, you should just take "a set is a collection of objects" as an informal idea of what sets are. Apart from the empty set, that phrase also has problems with collections of objects that are not sets because they are "too big", e.g. the collection of all sets is not a set.
Moreover, most of the sets considered in set theory aren't really sets of "objects" - they are sets of other sets. In the commonly studied set theories, there are no objects other than sets. This is another way that "a set is a collection of objects" can give the wrong impression.
So don't get hung up on the "a set is a collection of objects" phrase. Once you spend some time working with sets, you will have a better sense of what they are and how they work.