sets of numbers

[mr-HESHAM]

The first concept is the set

The set is Gathering distinct and well defined things, these things called the element of the set. In the set there is no need to repeat the elements for example A = {1, 2, 3, 4, 5, 6} this equal A = {1, 1, 2, 2, 3, 5, 6, 4}. We should note not all Gathering of things called set by mathematical meaning for example we can't call the important numbers, Beautiful girls and intelligent students are sets because we can't judge whether thing is belong or not belong to the set.



The second concept is belonging

It is said that a A If a is element of set A and it is said that a is not belongs to A Or a A If a is not element of the set A


Ex: A = {1, 2, 3, 4, 5, 6} then 1A and 4A but 7A because 7 not element of A
The set of numbers:



1) The real number set (R)
This set has four subsets :

• The natural number set

(N) = { 0,1,2,3,4,5,6,7,8,………….. } note that in somereferences N={ 1,2,3,4,5,6,7,8,………….. }.

• The integer numbers set

(I) = { …………,-5,-4,-3,-2,-1,0,1,2,3,4,5,……………………}.

• The rational numbers set

(Q) = {p/q, q≠0, p, qI} such as 5/6, 5/9, 10/9 and 12/7

• The irrational numbers set (Q*)

is the set of numbers cannot be written p/q and p/qI such as .






2) The complex numbers set (c)



x is called a complex number if x = a+ ib and i^2 = 1 and a ic called the real part of x and b is called the imaginary part of x


ex : x = 5 + 9i
real part = 5 and imaginary part = 9


x = 5 - 3i
real part = 5 and imaginary part = -3