Integers and Properties of Integers

I am sure we all are aware about integers; Let us recollect it again...

Integers: Integers are possitive and negative numbers. E.g. ...., -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6,..... Here each negative number is paired with a positive number the same distance from 0 on a number line.

Properties of Integers:

Below are some properties of Integers:

1. The sum of two integers is a integer
2. Addition on integers is cummutative, i.e a+b = b+a for all integers a,b
3. Addition of integers is associative, i.e. (a+b)+c = a+(b+c) for all integers a,b,c.
4. The integer zero, (0), is such that a+0 = a = 0+a for any integer a.
5. For any integer a, there correcponds an integer -a such that a+(-a) = 0 =(-a) +a
6. The product of any two integers is an integer.
7. Multiplication of integer is commutative i.e. a.b = b.a for any two integers a, b.
8. Multiplication of integers is distributive over addition i.e.
9. Multiplication of integers is associative, i.e. (a.b).c = a.(b.c) for all integers a,b,c.

a.(b+c) = a.b+a.c
(b+c) . a =b.a+c.a
for all integers a,b,c

10. The integer 1 is such that a.1 = a= 1.a for any integer a.


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