Download Number System and Closure Notes

ALGEBRA 1 – The Number System and Closure
Let’s draw a picture of what we just talked about!
Classify the following numbers by placing a check in the column to which groups they belong.
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.
______ 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, …
1
8
, 0.6,  , 5 …
2
3
YOUR TURN:
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:
Let’s look at an example of Closure: Integer + Integer = ________________
So we would say that integers are _______ under _________ 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:
So natural numbers are not closed under subtraction.
Your turn: 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.