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.
