Objective- To recognize different sets of numbers and to identify a domain. What is a set ? A set is a collection of objects called elements.
Living Things Bacteria Tree Diagram Whales Plants Animals
Mammals Reptiles Fish Humans Horses
Mr. Peterson
Brittany Spears
Venn Diagram
Quadrilaterals Trapezoids Parallelograms
Rhombuses
Squares
Rectangles
Sets of Numbers
Reals
can be written as a 2 , 7, -0 4 fraction. 3
Rationals - any number which
.
Irrationals - non-terminating
and 3141592... non-repeating . decimals
2
Fractions/Decimals
1 6 , -0 32, - 2 1 4
Integers
.
.
…-3, -2, -1, 0, 1, 2, 3...
Negative Integers
…-3, -2, -1
Wholes
0, 1, 2, 3...
Zero
0
Naturals
1, 2, 3...
Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Rationals
2 3
Reals
-2.65
Integers
-3
Wholes
-19
0 Naturals 1, 2, 3...
1 6 4
Irrationals
2
Imaginary Numbers
1
Rationals
2 3
Reals
-2.65
Integers
-3
Wholes
-19
0 Naturals 1, 2, 3...
1 6 4
Irrationals
2
Rule- the square root of any negative number will yield “No Real Solution”
Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) -6
Integer, Rational, Real
2) 5
7 Rational, Real 8
Natural, Whole, Integer, Rational, Real
3) 14 4) 6
Irrational, Real
Closure Property
A set of numbers is said to be „closed‟ if the numbers produced under a given operation are also elements of the set. The set of Whole numbers are closed under which operations? 3) Multiplication 1) Addition Closed 5 + 7 = 12 Closed 6+0=6 2) Subtraction Not Closed 4) Division Not Closed 5 - 7 = -2
Closure Property
A set of numbers is said to be „closed‟ if the numbers produced under a given operation are also elements of the set. The set of Integers are closed under which operations?
1) Addition Closed 5 + -7 = -2 -6 + 10 = 4 2) Subtraction Closed 5 - -7 = 12
3) Multiplication Closed 4) Division Not Closed
Domain- the set of values which may be meaningfully substituted for a given variable.
Which set of numbers would best describe the variable?
1) Let x = the number of people at a meeting. D: x Naturals
“ is a member of ”
2) Let y = your weight D: y Positive Reals
3) Let t = the low temperature in Alaska yesterday D: t Reals 4) Let n = the low recorded temperature in Alaska. D: n Integers
Graph t < 3 over the given domain.
1) D: Reals
-3 -2 -1 0 1 2 3 4
2) D: Integers
-3 -2 -1 0 1 2 3 4
3) D: Wholes
-3 -2 -1 0 1 2 3 4