1-1 Sets of Numbers - Math Slide Show

Lesson 1-1
Objective - To classify and order real
numbers.
Set- A collection of items or elements.
Element- one of the objects or members of a set.
Name the set of integers between -4 and 2.
{ −3, −2, −1, 0, 1}
Name a subset of this set.
{ −1, 0, 1}
Empty set- a set containing no elements.
∅ or
{ }
Finite set- a set that has a definite number of elements.
{ π , 23,0.23,0.2384
0.2384
}
Infinite set- a set that has an unlimited number
of elements.
{...− 3, −2, −1, 0, 1, 2... }
Methods for Representing Intervals
Numbers greater than 4.
x > 4
0 4
Interval Notation (4, ∞)
Methods for Representing Intervals
Numbers less than or equal to -2.
x ≤ −2
-2 0
Interval Notation
( −∞, −2]
Exclude endpoints
( )
Include endpoints
[ ]
Methods for Representing Intervals
Numbers between -1 and 6.
−1 < x < 6
-1 0 6
Methods for Representing Intervals
Numbers -3 through 6.
−3 ≤ x ≤ 6
-3 0 6
Interval Notation ( −1, 6)
Interval Notation [ −3, 6]
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010

Lesson 1-1 (cont.)
Set-Builder Notation
Write the integers between -4 and 6 in roster notation.
{ −3, −2, −1, 0, 1, 2, 3, 4, 5}
Set-Builder Notation
{ x −3≤ x≤5 and x∈Z}
∈−the element symbol.
Sets of Numbers
Naturals - Natural counting numbers
{ 1, 2, 3… }
Wholes - Natural counting numbers and zero
{ 0, 1, 2, 3… }
Integers - Positive or negative natural numbers or zero
{ … -3, -2, -1, 10123 0, 1, 2, 3… }
Rationals - Any number which can be written as a fraction.
Irrationals - Any decimal number which can’t be written as
a fraction. A non-terminating and non-repeating decimal.
Reals - Rationals & Irrationals
Sets of Numbers
Reals
Make a Venn Diagram that displays the following sets of numbers:
Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Rationals - any number which Irrationals- non-terminating
2 can be written as a
and
, 7, -0.4 fraction. π ≈ 3141592 . ... non-repeating
3 decimals
2
Fractions/Decimals Integers
1
, -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3...
6 1 4
Negative Integers Wholes
…-3, -2, -1 0, 1, 2, 3...
Zero
0
Naturals
1, 2, 3...
2
3
Reals
Rationals
Irrationals
Integers -2.65 π
-3
Wholes
-19
2
0
6 1 4 1.2121121112...
Naturals
1, 2, 3...
2
3
Reals
Imaginary Numbers
−1
Rationals
Irrationals
Integers -2.65 π
-3
Wholes
-19
2
0
6 1 4 1.2121121112...
Naturals
1, 2, 3...
Graphing Real Numbers on a Number Line
Graph the following numbers on a number line.
− 8 − 15 1 3 −0.2 π
11 4
-4 -3 -2 -1 0 1 2 3 4
− 8
− 15
11
−0.2
1 3 π
4
Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010