1. TN Standards
CLE Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies
CLE Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

2. Sec. P.1
Real Numbers

3. Classifying Numbers {1,2,3,4,…} {0,1,2,3,4,…} {…,-3,-2,-1,0,1,2,…}
Set of Natural numbers (counting #’s)
Set of Whole Numbers
Set of Integers
{1,2,3,4,…}
{0,1,2,3,4,…}
{…,-3,-2,-1,0,1,2,…}

4. Integers
Whole numbers
Natural numbers

5. Rational Numbers
Can be written as a ratio of 2 integers. (as a fraction)
Ex. ½ = .5, ⅓ = .333…, /111 = …
Either repeats or terminates

6. Rational Numbers
Integers
Whole numbers
Natural numbers

7. Irrational Numbers Cannot be written as a ratio of 2 numbers
Have infinite non-repeating decimal representations
Ex. √2 = ,
Π =

8. Real Numbers Irrational Numbers Rational Numbers Integers
Whole numbers
Natural numbers

9. Graphically real numbers are represented on a real number line with 0 being the origin, the right side of 0 is positive and the left is negative
Non negative
Either positive or zero
≈ means approximately equal to

10. Inequalities a < b means a is less than b
Same as b is greater than a
b > a
If a < b then a must be to the left of b on the number line

11. Look at Ex 4 p. 4 x is less than or equal to 2.
On the number line 2 has a bracket since it is included.
If a number is not included (does not have the =) then it has a parenthesis on the number

12. TN Standards
CLE Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies
CLE Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

13. Bounded Intervals Have a stopping place
a and b are the endpoints of the intervals (subsets of real numbers)
[a, b] means it includes (=) both a and b. This is said to be closed.
(a, b) means it does not include (not =) a or b. This is said to be open.
If one endpoint is included (=) but not the other, it is said to be half – open. [a, b) or (a, b]
Look at the box on the bottom of p. 3

14. Unbounded Intervals
Means it goes on forever in one direction or both directions.
∞ means infinity, -∞ means negative infinity
[a, ∞) half open x ≥ a
(a, ∞) open x > a
(-∞, b] half-open x ≤ b
(-∞, ∞) (entire real # line) open

15. Ex. 5 p. 5 A) c is at most 2 (Be careful) B) m is at least -3
Means c is 2 or less
c ≤ 2
B) m is at least -3
Means the least m can be is -3
m ≥ -3
C) All x in the interval (-3, 5]
Equal to 5 but not -3
-3 < x ≤ 5

16. TN Standards
CLE Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies
CLE Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.
CLE Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

17. Homework
P , odd, 95, 97