Fundamental Concepts of Intermediate Algebra
Topic: Axioms of Equality and Order
Property of Real numbers
- Equality - symbol is " = " and read as " equals " or " is equal to ", a statements that symbol or group of symbols which represents an equal quantity.
sample: a = a " a is equal to a itself " or " A quantity of a is equal to itself "
Properties of equality
The above example is an Reflexive Property of equality. Reflexive property is a quantity which reflect a it self, or a quantity which is exactly the same as it self.
example : Y + 7 = 7 + Y , p + 1 + z = 1 + z + p
Symmetric Property - it is where the first quantity is equal to the second quantity and reversible.
example : a = b so b = a
or a + b = 7 so b + a = 7
or 5 + c = 10 then c + 5 = 10
Transitive Property - when the quantity of the first is equal to the quantity of the second and the second is equal to the quantity of the third, then the quantity of the third is equal to the quantity of the first.
example : z = b , b = y then y = z
or a + 4 = b , b + 4 = a therefore a = b
Substitution Property - it is when the two elements are having the same quantity or equal with each other so you can replace element one to another element, and vice versa..
example: If y - 5 = z and y = a , then a - 5 = z
Every real number are having its pair of only point and its point is having only one real number. That point is associated with a line, and that is called a Line number.
Line number is helpful in knowing the relationship between numbers. And the number are called as coordinates of every points, and the points are the graphs of the numbers.
Transitive Property - it is always associated with a " greater than " or " > " and " less than " or " < ". When a first element is less that the second, and the second is less than the third, therefore the third is greater than the first.
example : when x < y , and y < z ,, therefore z > x.
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