Transcript Sec. P.1

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