let be the given set.
What are elements present in the set , where is super set of P
is superset of iff so,
Fernando Revilla
It is very important to understand that the above two are different. Think about how will you "define" ?
Your definition should be precise (basically you cannot say that it contanins nothing)
Once you do that you will understand the difference betweem the above.
Alright -
So now can you see the difference between
and
How many elements does each have?
PS: Though I am no expert on this subject but I feel has deep rooted significance - for e.g. you can question what do you mean by a set with 0 element? Maybe someone with more relevant knowledge can comment. But the two sets you mentioned are definately very different and it would be a blunder to consider they are same.
A note on why this topic is included in basic set theory.
The set contains two elements.
Both of the elements are sets. Neither a nor b is an element of .
Because
But we use the set to define the ordered pair .