Number System and its Fundamentals

Numbers:

The numbers written by symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are known as digits.

Even Numbers:
The numbers which are divisible by 2 are known as even numbers. e.g. 12, 24, 68 . . . . . . so on.

Odd Numbers:
The numbers which are not divisible by 2 such as 3, 5, 7 and so on are known as odd numbers.

Natural Numbers:
The numbers which are used for counting {such as 1, 2, 3, 4, 5, 6, 7 . . . . . so on.} are known as Natural numbers. The positive integers are also known as natural numbers.
Thus 4567 is a natural number but 0, -3, 14.6, $$\frac{3}{4}$$ etc. are not natural numbers.

Whole Numbers:
If zero is included in natural numbers, the set so obtained is known as whole numbers.
W = {0, 1, 2, 3, 4, 5, 6 . . . . . . so on.}
But -1, -2, 5.6, $$\frac{1}{9}$$ is not a whole number.

Integers:
The whole numbers are positive as well as negative which is known as integers.
I = {-1, -2, -3 . . . . . . 0, 1, 2, 3, 4 . . . . . . so on.}
But $$\sqrt 6 $$ , 0.32, -1.4, $$\frac{3}{4}$$ etc. is not integers.

Rational Numbers:
The numbers which can be expressed in the form of $$\frac{{\text{p}}}{{\text{q}}}$$, where p and q are integers but q is not equal to 0, are known as rational numbers. For example 26, -45, $$\frac{{56}}{{345}}$$ , $$ - \frac{3}{8}$$ etc are rational numbers.

Irrational Numbers:
A number which cannot be expressed in terminal decimals are known as an irrational numbers. For example $$\sqrt 8 $$ , 3 + $$\sqrt 2 $$  etc. are irrational numbers.

Real numbers:
The numbers either rational or irrational are known as real numbers. For example, 3, $$\sqrt 7 $$  etc. are the real numbers.

Prime Number:
A natural number other than 1 is a prime number if and only if it is divisible by 1 and the number itself.
For example: 2, 3, 5 etc. are Prime but 6, 8, 20 etc. are not prime numbers.

Composite Number: The natural number other than 1 is a composite number which is divisible by 1, the number itself and at least one more other number. For example, 8 is a composite number because it is divisible by 1, 2, 4 and 8.

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