ما هي مجموعة الأعداد الحقيقيه ( ح ) ؟

 The real numbers (H)  are the numbers that consist of the

 union of rational numbers and irrational numbers, and we will

 identify in This article is what real numbers are and we will

 learn about the properties of real numbers such as addition,

 subtraction, multiplication and division of numbers Real

 numbers, real numbers, subdivisions, intersection and union,

 and the difference between groups, and we will get to

 know all of that and more.In the Mathematics in English

?What is the definition of real numbers

They are numbers that can be written in the form of fractions

 such as 1/2 and can be written in the form of decimal

 numbers such as 4,3 and consist of the union of a group

The union of integers, the union of irrational numbers, the

 union of relative numbers, the union of natural numbers, the

 union of counting numbers and all these groups

Partial sets of real numbers and the set of real numbers is an infinite set of numbers

Sections of Real Numbers (H)

1. Relative numbers are numbers written in numerator and denominator form, such as 4/5
2. Irrational numbers are numbers that cannot be written as a numerator or denominator, and have no roots
3. Mixed numbers are numbers that fall into the category of whole numbers
4. Whole numbers are numbers that are formed by the combination of the natural numbers and zero
5. Whole numbers are numbers that have neither fractions nor decimal numbers, and are divided into positive and negative integer numbers, the union of zero.
6. The natural numbers are the numbers that consist of the one to the infinite

?What are the subsections of the real numbers group (h)

• Even real numbers are numbers that can be divided by 2 and an even number one of these numbers (0, 2, 4, 6, and 8).
• Individual real numbers is every number that cannot be divided by 2 without a remainder, or it is every number that is not a multiple of the number 2, is it the number of an odd number one of these numbers (1, 3, 5 and 7)
• Positive numbers are numbers greater than zero, such as 5
• Negative numbers are numbers less than zero, such as -4
• Prime numbers are numbers that are divisible by 0 and 1
• Complex numbers are numbers that contain all the roots of a quadratic equation

Important notes

1. The set of real numbers is denoted by the symbol (H)
2. The group of rational numbers is denoted by the symbol (n)
3. The group of irrational numbers is denoted by the symbol (n-)
4. The set of integers is denoted by the symbol (r)
5. The group of natural numbers is symbolized by the symbol (i)
6. The set of positive integers is denoted by (y +)
7. The set of negative integers is denoted by the symbol (p-)
8. The group of counting numbers is symbolized by the symbol (p)

Intersection, union and difference between groups

• N union n- = h
• N and n- partial of h
• I and r are partial of h
• N junction n- = phi
• H difference n- = n
• H + zero union h- = h
• Y - y- = i
• Y - i = r-
• Y + p-junction - = phi
• I union p - = p
• I union p + = i
• I - p = phi
• R- - p = phi
• P - p = phi
• P - p = phi
• I - i = phi
• H - h = phi

Properties of real numbers (h)

Addition of real numbers

The commutative property is a property that is possible in

 addition where a real number + a real number = a real

 number such as 8 + -1 = 7 and the seven is a real number at

Using the wildcard property, it is as follows: -1 + 8 = 7, and the

 seven is a real number. We conclude that the addition is a possible operation

The closing property is a property that is possible in addition

 where (real number) + real number = real number such as (-4) + 1 = -3 and negative 3 is a number

It is true that we conclude that closure is a possible property in

 combination Combining in addition is a possible operation

 because commutation is a possible operation in addition The

 additive neutral in mathematics is zero, meaning that when

 adding any number with zeros, it produces the same

 number The additive inverse means we change the sign of

 the number like the additive inverse of 5 is -5

Important notes in the collection

1. A positive real number + a positive real number = produces a real number that is greater than the numbers you added
2. A real negative number + a positive real number = produces a real number and its sign according to the larger number
3. A real negative number + a real negative number = a real negative number and the resulting number is smaller than the two numbers that added

Subtracting the real numbers

The commutative property is a property that is not possible in

 subtraction where when switching any two numbers another

 number is produced such as 5 - 7 = -2 and 7 - 5 = 2 results

Different people conclude that the swap operation is not

 possible The closing property is a possible property in

 subtraction,  whereby when any two numbers are subtracted,

 a real number is produced The merge property is a property

 that is not enabled in subtraction since the substitution is not possible in subtraction

Important notes in the offering

1. Negative real number - negative real number = negative real number
2. If a negative number occurs after subtraction, we change the subtraction sign to addition

Multiplying real numbers

The commutative property of multiplication is a possible

 operation, as the transposition of the multiplication of any two

 real numbers produces an integer such as 5 x 4 = 20

 and When you multiply 4 x 5 = 20, we deduce that the

 substitution is a possible operation in multiplication The

 closed property of multiplication is possible, where when you

 multiply any two numbers in the following way, an integer

 such as 2 x (3) = 6 is produced. We conclude from the

 example. Previous that the process of closure is possible in

 beating The merging property in multiplication is a possible

 operation because the commutation is a possible operation in

 multiplication The multiplicative neutral is the integer one,

 meaning when multiplying any integer x 1 = the same integer as 7 x 1 = 7

Important notes on multiplication

1. A positive real number x a positive real number = a positive real number
2. A positive real number x a negative real number = a negative real number
3. A negative real number x a negative real number = a positive real number

Division of real numbers

The commutative property is a property that is not possible in

 the division, where when switching and dividing any two

 numbers results in another number such as 8/4 = 2 and 4/8 =

 1/2 The two results are different. We conclude that the

 commutative property is not possible in division The closing

 property is possible in division, where when dividing 8 / -12 =

 2/3 belongs to the set of real numbers, we conclude that the

 operation Closure is possible in the division

The merge property is a property that is not possible in the

 division as the substitution is not possible in the division

Important notes on the division of real numbers

1. Positive real number / positive real number = positive real number
2. Positive real number / negative real number = negative real number
3. A real number / a positive real number = a negative real number
4. Negative real number / negative real number = positive real number

Examples

Find the solution set in (h )                       2 x 2 - 4 = 4

Solve the following equation                       2 x 2 = 4 + 4

2/ 2x2 =8                                in division 

X 2 = 4 From this equation we deduce that x = positive or negative 2

Solution group in h = group 2 and -2

is 0 a real number 

Zero is one of the most important real numbers