Questions and Answers
What is closure?
The property of an operation and a set that the performance of the operation on members of the set always yields a member of the set.
What are integers?
Numbers {0, +1, -1, +2, -2,...} designated with ℤ.
What are irrational numbers?
Real numbers which cannot be written as the ratio of two integers; designated with ℚ'.
What are natural numbers?
Signup and view all the answers
What are rational numbers?
Signup and view all the answers
What are real numbers?
Signup and view all the answers
What are whole numbers?
Signup and view all the answers
_____ are the rational numbers together with the irrational numbers; designated with ℝ.
Signup and view all the answers
_____ are numbers of the form {a/b ∣ a,b ∈ ℤ, b ≠ 0} and designated with ℚ.
Signup and view all the answers
_____ are numbers {0, +1, -1, +2, -2,...} designated with ℤ.
Signup and view all the answers
Numbers {0, 1, 2, 3, 4,...} are called __.
Signup and view all the answers
____ are numbers {1, 2, 3, 4,...} and designated with ℕ.
Signup and view all the answers
____ are real numbers which cannot be written as the ratio of two integers; designated with ℚ'.
Signup and view all the answers
____ is the property of an operation and a set that the performance of the operation on members of the set always yields a member of the set.
Signup and view all the answers
Is $ ext{√2}$ rational or irrational?
Signup and view all the answers
Is $ ext{π}$ rational or irrational?
Signup and view all the answers
Is $5$ rational or irrational?
Signup and view all the answers
Is $0.333...$ rational or irrational?
Signup and view all the answers
Identify the set: {-2, -1, 0, 1, 2}.
Signup and view all the answers
Identify the set: {0, 5, 10, 15}.
Signup and view all the answers
Identify the set: {4, 5, 6, 7}.
Signup and view all the answers
Identify the set: {0, 8, 9, 10}.
Signup and view all the answers
Identify the set described: It is closed under addition and multiplication but not closed under subtraction or division.
Signup and view all the answers
Identify the set described: It is closed under addition and subtraction, multiplication, and division, with the exception of division by 0 which is not defined.
Signup and view all the answers
Study Notes
Closure
- Represents the property of an operation and a set where performing the operation on elements always results in an element of the same set.
Integers
- Includes numbers {0, +1, -1, +2, -2,...}, denoted by ℤ.
Irrational Numbers
- Real numbers that cannot be expressed as a ratio of two integers; designated with ℚ'.
Natural Numbers
- Consist of positive integers {1, 2, 3, 4,...}, represented by ℕ.
Rational Numbers
- Defined as numbers in the form {a/b | a, b ∈ ℤ, b ≠ 0}, including zero and denoted by ℚ.
Real Numbers
- A combination of rational and irrational numbers, represented by ℝ.
Whole Numbers
- Include all non-negative integers {0, 1, 2, 3,...}.
Rational Identification
- Examples of rational numbers include integers and terminating or repeating decimals (e.g., 5 and 0.333...).
Irrational Identification
- Examples of irrational numbers include non-repeating decimals that cannot be expressed as fractions (e.g., √2 and π).
Set Identification
- Sets {−2, −1, 0, 1, 2} represent integers.
- Sets {0, 5, 10, 15} include whole numbers and integers.
- Sets {4, 5, 6, 7} contain natural numbers, whole numbers, and integers.
- Sets {0, 8, 9, 10} consist of whole numbers and integers.
Natural Numbers and Operations
- Natural numbers are closed under addition and multiplication, but not under subtraction or division.
Real Numbers and Operations
- Real numbers form a complete set closed under addition, subtraction, multiplication, and division, with division by zero undefined.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore the foundational concepts of real numbers and their subsets with this flashcard quiz. Each card provides key definitions and properties essential for understanding algebraic structures. Perfect for reinforcing your knowledge in Algebra II.
