Number System

 Real Number:
All numbers whether rational and irrational comes under the category of real number
Example: 1,500.22/3,1/3,√2 etc.

Rational Numbers:
A number that can be represented in the form p/q where p and q are integers and q is not zero.
Example: 2/3, 1/10, 8/3 etc. They can be finite decimal numbers, whole numbers, integers, fractions.

Irrational Number:
An irrational number is a number that cannot be written as a ratio (or fraction).  In decimal form, it never ends or repeat.
Example: √2,π, Other famous irrational numbers are the golden ratio, a number with great importance to biology:
\varphi = \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots.

Numbers with no fractional part i.e. q=1 in p/q form (always).It includes:
All Counting  Numbers(1,2,3,4,5,6,……), ZERO(0) & Negative of  all counting Numbers(-1,-2,-3,-4,-5,-6,……..)

Natural Number:
The natural (or counting) numbers are 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.

Even numbers: 
The numbers divisible by 2 are even numbers. e.g., 2, 4, 6,8,10 etc. Even numbers can be expressed in the form 2n where n is an integer other than 0.

Odd numbers: 
The numbers not divisible by 2 are odd numbers. e.g. 1, 3, 5, 7, 9 etc. Odd numbers are expressible in the form (2n + 1) where n is an integer other than 0.

Composite numbers: 
A composite number has other factors besides itself and unity .e.g. 8, 72, 39 etc. A real natural number that is not a prime number is a composite number.

Prime numbers: 
The numbers that has no other factors besides itself and unity is a prime number.
Example: 2, 23,5,7,11,13 etc. Here are some properties of prime numbers:

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