January 31, 2011
P1: Real Numbers
January 31, 2011
A real number is any number that can be written as a
decimal. They can terminate, repeat, or continue
endlessly with no discernible pattern.
Subsets of the set of real numbers include:
natural numbers
whole numbers
integers
January 31, 2011
Rational numbers are real numbers that can be
written as a ratio of two integers. They will either
terminate or repeat. A real number that neither
terminate nor repeats is called an irrational number.
January 31, 2011
Interval Notation - bounded intervals
[a, b] means a ≤ x ≤ b. This is a closed interval
because the endpoints are included in the interval.
ex: Graph the interval [−2, 3]. Write in inequality
notation.
(a, b) means a < x < b. This is an open interval
because the endpoints are not included in the
interval.
ex: Graph the interval (-4,1). Write in inequality
notation.
January 31, 2011
An interval may be open on one side and closed on the other
such as (0, 5]. Write this as a compound inequality.
January 31, 2011
Interval Notation - unbounded intervals
The set of all real numbers greater than π is an
unbounded interval since there is no largest real
number. The interval notation for this set of numbers is
(π, ∞). If we want to include the number π in our
interval we write [π, ∞). Since the symbol ∞ does not
represent a number it would never be appropriate to
use a square bracket next to the infinity sign.
Write inequality and interval notation for each graph.
January 31, 2011
Properties of the Exponents
January 31, 2011
Simplify the expression.
January 31, 2011
January 31, 2011
HW: p.11-12 #5-31 odd, 47,49,51