Axioms of Inequality and Real Number Line


Vocabulary and Rules
Real Numbers-The set of numbers on a number line
Graph-A number line showing the relationship of a set of numbers
Rule-Every point on a number line represents one and only one real number
Rule-Every real number is represented by one and only one point on a number line

Axiom
Example
Axiom 1: If a<b and b<c, then a<c
3 < 5 and 5 < 7, then 3 < 7
Axiom 2: If a<b, then a + c < b + c
3 < 5
3 + 4 < 5 + 4
7 < 9
Axiom 3: Positive Number
If a < b and 0 < c, then ac < bc
3 < 5
3 * 2 < 5 * 2
6 < 10
Axiom 4: Negative Number
If you multiply both sides of an inequality by a negative number, you change the direction of the inequality
3 < 5
3 * -3 ? 5 * -3
-9 > -15
Graphing Inequalities:
Open circle on the value and you shade the direction the inequality points