Download 64 2 3 27 ALGEBRA 1 – The Number System and Closure

ALGEBRA 1 – The Number System and Closure
Let’s draw a diagram of what
we just talked about!
Classify
Number
Counting
Number
Whole
Number
Integer
Rational
Number
Irrational
Number
5
0.4
64
2
3
27
-2
Match the sets of numbers.
______ 1. Whole Numbers
a. -1, -2, -3, -4,…
______ 2. Integers
b. 1 ,0.6,  8 ,5 …
______ 3. Positive Integers
c. 0, 1, 2, 3, 4, …
______ 4. Negative Integers
d. 1, 2, 3, 4, …
______ 5. Rational Numbers
e. -4, -3, -2, -1, 0, 1, 2, 3, 4, …
2
3
With your Partner:
6.
Name a number that is an integer but not a whole number. ________________
7.
Name a number that is rational but not a counting number. ________________
8.
Name a number that is whole but not counting. _______________________
9.
Name a number that is counting but not whole. ______________________
10.
TRUE or FALSE: All whole numbers are integers. ___________________
11.
TRUE or FALSE: All integers are whole numbers. ___________________.
12.
TRUE or FALSE: Every real number is rational. ___________________
Closure:
A set has closure under an operation if the operation is performed on elements of the set
and the result is in the original set. Say What?!!?! OK, we need to define some terms.
Set:
Operation:
Elements:
Example of Closure:
Integer + Integer = ____________________
So we would say that integers are ________________________________________________because we can pick ANY two
_______________________ and ____________________ them and we end up with another _____________________.
IMPORTANT!! If we want to say that a statement is false we need to provide a _________________________.
Example: are natural numbers closed under subtraction?
True example:
Counter-example:
Decide with your partner whether the following statements are true or false. If it is not true give a
counter-example:
1) Integers are closed under multiplication.
2) Integers are closed under division.
3) Rationals are closed under multiplication.
4) Whole numbers are closed under division.
HW: on a half sheet of paper come with TWO statements about closure. One statement should be true,
and the other should be false with a counterexample.