![Geometric Interpretation
{ 6 4}x x− < ≤
(-6,4]
0-6 4
( ]
Interval
notation](https://image.slidesharecdn.com/06-orderingofthesetofrealnums-150826011807-lva1-app6891/85/06-ordering-of-the-set-of-real-nums-13-320.jpg)
![Geometric Interpretation
{ 1 9}x x≤ ≤
[1,9]
0 1 9
[ ]](https://image.slidesharecdn.com/06-orderingofthesetofrealnums-150826011807-lva1-app6891/85/06-ordering-of-the-set-of-real-nums-14-320.jpg)
![Geometric Interpretation
(a,b) [a,b]
(a,b] [a,b)](https://image.slidesharecdn.com/06-orderingofthesetofrealnums-150826011807-lva1-app6891/85/06-ordering-of-the-set-of-real-nums-15-320.jpg)
![Geometric Interpretation
(a,+∞) [a,+∞)
(- ∞,b] (- ∞,b)
How do we represent it in a real
number line?](https://image.slidesharecdn.com/06-orderingofthesetofrealnums-150826011807-lva1-app6891/85/06-ordering-of-the-set-of-real-nums-16-320.jpg)
![Geometric Interpretation
(- ∞,b]
b
]](https://image.slidesharecdn.com/06-orderingofthesetofrealnums-150826011807-lva1-app6891/85/06-ordering-of-the-set-of-real-nums-19-320.jpg)
06 ordering of the set of real nums
- 1. Math 11 Ordering of the set of real numbers
- 2. The symbols < and > < > Less than Greater than
- 3. The symbols < and > • If a and b are real numbers 1.a < b if and only if b – a is positive a = 10 and b = 15
- 4. The symbols < and > • If a and b are real numbers 2.a > b if and only if a-b is positive a = 22 and b = 8
- 5. The symbols ≤ and ≥ ≤ ≥ Less than or equal to Greater than or equal to
- 6. <, >, ≤ and ≥ < > ≤ ≥ Strict inequalities Non Strict inequalities
- 7. Continued Inequality • If a < x and x < b then a < x < b a = 5, x = 8 and b = 10
- 8. Inequalities and Set Notation The set of all x such that x is greater than -9 and less than 8 {x | 8 > x > -9 }
- 9. Inequalities and Set Notation {x | 2x+ 4 ≥ 0} The set of all x such that 2x+4 is nonnegative.
- 10. Inequalities and Set Notation The set of all a such that a-2 is greater than -5 and less than or equal to 7 {a | 7 ≥ a – 2 > -5 }
- 11. Inequalities and Set Notation {z | 15 ≥ 2z+5 ≥ -1} The set of all z such that 2z+5 is between and including -1 and 15.
- 12. Geometric Interpretation Origin = 0 REAL NUMBER LINE 0
- 13. Geometric Interpretation { 6 4}x x− < ≤ (-6,4] 0-6 4 ( ] Interval notation
- 14. Geometric Interpretation { 1 9}x x≤ ≤ [1,9] 0 1 9 [ ]
- 16. Geometric Interpretation (a,+∞) [a,+∞) (- ∞,b] (- ∞,b) How do we represent it in a real number line?
- 21. Inequalities and Set Operations { | 2} { | 12}x x x x> ∪ < What if we combine set operations and inequalities?
- 22. Inequalities and Set Operations { | 2} { | 12}x x x x> ∩ < { | 3} { | 10}x x x x> ∪ <
- 23. inequalities and set operations { | 8} { | 0}x x x x> − ∩ ≤