# Set of Complex Numbers

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The set of complex numbers is a set of all numbers ever existed, from pi to 1.

## Complex Numbers

Complex numbers are numbers which have a real part and an imaginary part, usually written in the from a + b $i$.

### Real Numbers

Real numbers is the set of all numbers which aren't imaginary, eg. don't have the b $i$ counterpart and can be squared into some nonnegative number.

### Imaginary Numbers

Imaginary numbers is the set of numbers which do have the b $i$ 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

Irrational numbers are all numbers which cannot be simplified into the from a/b where b isn't 0.

### Rational Numbers

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

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

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.