sets of numbers

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 some references 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 

wish to be useful
mr Hesham

why x ^zero = 1

Not many students know the cause of it but it is very simple

 (10000^ zero) = 1 because 10000^zero = 10000^(1-1)= 10000^1 /10000^1 = 1

very easy 

operations on Fractions: addition &subtractuon

first if the denominators are similar then we just add the numerator

ex : 3/5  + 6/5 

here the denominators are similar then total is (3+6)/5=9/5

ex 2: 12/7 + 5/7=  17/7

ex3:   6/5   - 7/5=   -1/5

second if the denominators are not similar then we should make Unification denominators before make the operation

ex :  3/2 + 5/3 = 

( (6/2)× 3  + (6/3) ×  2  )  /(2 ×3)= ( 4 + 9 ) / 6 = 13 / 6

ex: 5/6 - 7/8 = 

((40/6)× 5 - (40/8) × 7) / ( 6×8)=  ( 48 - 35 ) / 40 =13 / 40

very easy 

enjoy

mr Hesham

Fractions

A Fraction consists of two numbers separated by a line. 

the top number called numerator  and the Bottom called denominator

 ex : 3 / 10 

numerator = 3 and denominator = 10

to get the meaning of fractions and its importance ,Suppose that we want to Divide three oranges on ten person then we say 3 / 10  the numerator is 3 and the denominator is 10 

ex :  divide 5 apples on 3 persons 

     5 is numerator and 3 is denominator  or  3/5

easy way to understand Addition and subtraction

 When we explain the addition and subtraction to a child, in some cases have difficulty in understandingThis is an easy way I use it with the kids give me great resultsI  hope to be helpful to you

We consider the  positive number as profit and consider the negative number as loss

ex : 4 = we gained  4  and  - 4 = we loss 4 

ex : 4 + 4 

here the two number are positive then we gained 4 and 4 then we gained 8 

ex :  -4  +  6  

here   4 is negative (loss) but 6 is positive (profit) then i gained 6 but loss 4 then i gained 2 = +2

  

ex :  9 - 5

here i have 9 as profit but i lost 5 then i gained 4 = +4 

enjoy

mr Hesham