2. Introduction to integer’s
system
At any vhole number a and b if
there is a single element is
always added up (a + b) which
is the whole numbers. It is said
that the system of whole
numbers is closed under
addition. But not also with
subtraction and division
4. Integer’s principle
Closed under Principle of addition
The closed Principle of the
multiplication
Commutative Principle of addition
Commutative Principle of
multiplication
Associative Principle of addition
Associative Principle of
5. The left distributive principle of
multiplication over addition
The right distributive principle of
multiplication over addition
For every a, with elements 0 in B so a
+ 0 = a, 0 is called the additive identity
element
For every a, with element 1 in B such
that ax 1 = a, 1 called elements
multiplicative identity
Feedback (inverse)
6. Addition of
integer’s If a and b are positive integers, then (-
a) + (-b) = - (a + b)
If a and b are positive integers with a
<b, then a + (-b) = - (b - a)
a+(-b)=-(b-a) kanselasi Principle of
addition
If a, b, and c integers and a + c = b +
c, then a = b
7. Subtraction of integers
If a, b and k integers, then a - b = k if and
only if a = b + k. subtraction in numbers has
not minced closed nature, ie if a and b are
the numbers count, (ab) there (whole
numbers) only if a> b
According to the definition of subtraction a - b
= k if and only if a = b + k
a + (-b) = (b + k) + (-b)
= (k + b) + (-b)
= k + (b) + (-b)
= k + 0
a + (-b) = k
k = a + (-b)
This indicates that there is an integer k such
that a - b = k
9. Division of integers
Formulas:
((-a) : b) x (b) = (-a)
(a : (-b)) x b = (-a)
((-a) : b) x (-b) = a
(a : (-b)) x (-b) = a
((-a) : (-b)) x b = a
((-a) : ( -b)) x (-b) = (-a)
