# Number System Short Notes

#### Number System Short Notes

1. Number 1 is neither divisible nor prime.
2. Two consecutive odd prime numbers are called prime pair.
3. All natural numbers are whole, rational, integer and real.
4. All whole numbers are rational Integer and real.
5. All whole numbers are rational and real.
6. All rational numbers includes the integers, since every integer can be written as a fraction with denominator 1. Example (7/1) not only 7
7. All whole numbers, rational and irrational numbers are real.
8. Natural (including Prime, Composite, even or odd) numbers and whole numbers are never negative.
9. Any Prime Number can never be a Composite Number.
10. Fractions are rational.
11. All prime number except 2 are odd. Or 2 is the only even prime number.
12. Zero (0) is neither negative nor positive number.
13. If a is any number then, if a divides zero, result will be zero. If 0 divides a, then result will be infinite or not defined or undetermined i.e.
0/a =0, but a/0 =∞ (infinite)
where a is real number.
14. The sum and the product of two rational number is always a rational numbers.
15. The product or the sum of a rational number and irrational number is always an irrational number.
16. Pie (π) is an irrational number.
17. There can be infinite number of rational or irrational numbers between two rational numbers or two irrational numbers.
18. Decimal indication of an irrational number is infinite coming. as−√3,√2as−3,2The square of an even is even and the square of an odd number is odd.