Set of Complex Numbers
The set of complex numbers is a set of all numbers ever existed, from pi to 1.
Complex numbers are numbers which have a real part and an imaginary part, usually written in the from a + b.
Real numbers is the set of all numbers which aren't imaginary, eg. don't have the b counterpart and can be squared into some nonnegative number.
Imaginary numbers is the set of numbers which do have the b counterpart. They will always be squared into a negative number.
Set of all Real Numbers
The set of all real numbers can be classified into two major sub sets, the set of irrational and rational numbers.
Irrational numbers are all numbers which cannot be simplified into the from a/b where b isn't 0.
Rational numbers are all numbers which can be simplified into a/b. The rational numbers can be further split into to more subsets, subsubsets, and so on.
Set of Real Numbers
Integers are all numbers which aren't fractions but can be simplified into a/b. For example, 2 is an integer and 2/3 isn't. Usually integers are numbers we use for our daily counting. They are both negative and nonnegative.
Natural numbers are all positive integers. Examples are 2 and 3. 0 is nonnegative, but isn't positive so is therefore excluded. Natural numbers are a subset of integers, which are a subset of rational numbers, which combine with irrational numbers to make real numbers, which combine with imaginary numbers to make the set of all complex numbers.