Hello viewers...

If you want to learn about basic Number system in Maths, then check out this post carefully. I made a diagram to understand it so easily. This one image is enough to understand you number system.



Now let's discuss this all number with definition.

The Natural Numbers:

Counting numbers are called Natural numbers. These are the numbers we use in daily life for counting anything like 1,2,3,4,5, etc. There are infinitely many natural numbers. The set of natural numbers, {1,2,3,4,5,...}, is sometimes written N for short

The sum of any two natural numbers is also a natural number (for example, 4+2000=2004), and the product of any two natural numbers is a natural number (4×2000=8000). This is not true for subtraction and division, though.

The Whole Numbers:

The whole numbers are the natural numbers together with 0.

The Integers:

The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero.

{...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...}
The set of integers is sometimes written J or Z for short.

The sum, product, and difference of any two integers is also an integer. But this is not true for division... just try 1÷2.

The Rational Numbers:

The rational numbers are those numbers which can be expressed as a ratio between two integers. For example, the fractions ⅓  and −⅞ are both rational numbers. All the integers are included in the rational numbers, since any integer z can be written as the ratio z/1 

All decimals which terminate are rational numbers (since 8.27 can be written as 827/100.) Decimals which have a repeating pattern after some point are also rationals: for example,

0.0833333....=1/12.

The set of rational numbers is closed under all four basic operations, that is, given any two rational numbers, their sum, difference, product, and quotient is also a rational number (as long as we don't divide by 0).

The Irrational Numbers:


An irrational number is a number that cannot be written as a ratio (or fraction).  In decimal form, it never ends or repeats. The ancient Greeks discovered that not all numbers are rational; there are equations that cannot be solved using ratios of integers.

 is about 1.414, because , which is close to . But you'll never hit exactly by squaring a fraction (or terminating decimal). The square root of  is an irrational number, meaning its decimal equivalent goes on forever, with no repeating pattern:


Other famous irrational numbers are the golden ratio, a number with great importance to biology:


 (pi), the ratio of the circumference of a circle to its diameter:


and , the most important number in calculus.


Irrational numbers can be further subdivided into algebraic numbers, which are the solutions of some polynomial equation (like  and the golden ratio), and transcendental numbers, which are not the solutions of any polynomial equation.  and  are both transcendental.

The Real Numbers:

          The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.  The real numbers are “all the numbers” on the number line.  

There are infinitely many real numbers just as there are infinitely many numbers in each of the other sets of numbers.  But, it can be proved that the infinity of the real numbers is a bigger infinity.