There are various number types that we deal with in math, specially in algebra:

## Natural Numbers

those we got introduced to while learning counting as young children. They start from 1 and go all the way to infinity, i.e., 1, 2, 3, 4, 5, 6, etc. They are also called positive integers.

## Whole Numbers

If you add ‘0’, i.e., 0, 1, 2, 3, 4, 5, 6, and so on. Then this set is called the set of Whole Numbers.

## Integers

The next important number type is Integers. If you write all the whole numbers and their negative counterparts, i.e., -∞, …, -3, -2, -1, 0, 1, 2, 3, …∞ , then all these numbers are called integers. We can say that all whole numbers and natural numbers are integers, but not vice versa.

## Fractions

A fraction represents parts of a whole number. It can be written in the form m/n, where both m and n are whole numbers, and n cannot be 0. Once again, all fractions are rational numbers, but not vice versa. Those fractions are termed as proper that have the numerator smaller than the denominator; if, on the other hand, the numerator is greater than the denominator, then the fraction is termed as the improper one. Example: 2/3 is a proper fraction, and 3/2 is an improper fraction. All terminating decimals numbers and *some *repeating decimals can be written as fractions. You can write the terminating decimal 1.28 as 128/100 = 32/25. While repeating decimal 0.333333… can be written as 1/3, but 0.4444444… does not yield that elegant an answer though you can still express it as 1/2.2500002250000.

## Rational Numbers

Rational Numbers are those numbers that can be represented in the form of m/n, where n≠0. The number m/n can be further simplified and represented in decimal form. The set of rational numbers includes positive, negative numbers, and zero. Some examples of rational numbers; are 10/2 (=5), 1/100 (=0.01), and 60/10 (=6).

## Irrational Numbers

On the other hand, Irrational Numbers are those numbers that cannot be written in fraction form or the ratio of the two integers. A few examples of irrational numbers are √2, √3, √5, … π, etc.

## Real Numbers

The set of rational and irrational numbers is called the set of Real Numbers.

## Imaginary Numbers

Numbers other than real numbers are imaginary or complex numbers. When we take the square of an imaginary number, it gives a negative result, which means it is a square root of a negative number, for example, √-2 and √-3. When we square these numbers, the results are -2 and -3. The square root of -1 is represented by the letter i, which means i = √-1. When a real number gets combined with an imaginary number, a Complex Number is expressed as m + ni or m + n√-1.

For a more detailed list, check Wikipedia page on Number types in Math.