TN Standards CLE 3124.1.5 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 3124.1.6 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 3124.2.2 Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

Sec. P.1 Real Numbers

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,…}

Integers Whole numbers Natural numbers

Rational Numbers Can be written as a ratio of 2 integers. (as a fraction) Ex. ½ = .5, ⅓ = .333…, 125/111 = 1.126126… Either repeats or terminates

Rational Numbers Integers Whole numbers Natural numbers

Irrational Numbers Cannot be written as a ratio of 2 numbers Have infinite non-repeating decimal representations Ex. √2 = 1.4142136..., Π = 3.1415927...

Real Numbers Irrational Numbers Rational Numbers Integers Whole numbers Natural numbers

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

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

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

TN Standards CLE 3124.1.5 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 3124.1.6 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 3124.2.2 Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

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

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

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

TN Standards CLE 3124.1.5 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 3124.1.6 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 3124.2.2 Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

Homework P. 12 1-4, 11-49 odd, 95, 97