The concept of a set of numbers is very simple: it is simply a collection of numbers. That is all it is. The set may contain infinitely many numbers, or just a finite lot of them, even one or none. The numbers in the set may have some relationship with one others in the set or they may be no such relationship.
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Many infinite sets appear in mathematics: the set of counting numbers; the set of integers; the set of rational numbers; the set of irrational numbers; the set of real numbers; the set of complex numbers. Also, certain subsets of these, such as the set of square numbers, the set of prime numbers, and others.
The basic concepts are:a setsome elements, anda rule which can be used to decide whether or not a particular element belongs to the set.
In a certain sense, the set of complex numbers is "larger" than the set of real numbers, since the set of real numbers is a proper subset of it.
All of the natural numbers.
The set of integers, the set of rational numbers, the set of real numbers, the set of complex numbers, ...