Download Integrated Algebra - Name NOTES: The Closure Property Date

Integrated Algebra -
Name
NOTES: The Closure Property
Date
Today’s Objective
 Review the subsets of the Real Number system.
 Understand the closure property and how it applies to the Real Number system.
The Property of Closure
A set is said to be CLOSED under a binary operation when every pair of elements from a
set, under a given operation, yields an element from that set.
Binary Operations
Examples:
Subsets of the Real Number System
Real Numbers:
Rational Numbers:
Integers:
Whole Numbers:
Natural Numbers:
Properties of Number Sets
•
The sets of whole numbers, rational numbers, and real numbers are
•
The sets of integers, rational numbers, and real numbers are
•
The sets of nonzero rational numbers and nonzero real numbers are
Examples:
1. Does the closure property hold for the set of negative integers under multiplication?
Addition?
2. Does the closure property hold for each of the following sets under the given
operation? Justify your answers.
a. Whole numbers; Multiplication
b. {1, 2, 3}; Addition
c. Real numbers; Subtraction
d. Whole numbers; Subtraction