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Questions and Answers
What is an integer?
What is an integer?
A whole number, either positive, negative, or zero, without a fractional part.
What operation is not closure for integers?
What operation is not closure for integers?
Division
What is another term for positive integers?
What is another term for positive integers?
Natural numbers
What is the set of integers represented as?
What is the set of integers represented as?
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What is the result of the addition of two integers?
What is the result of the addition of two integers?
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What is a non-positive integer?
What is a non-positive integer?
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Study Notes
Definition
- An integer is a whole number, either positive, negative, or zero, without a fractional part.
- It is a member of the set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Properties
- Integers are closed under addition, subtraction, and multiplication, meaning that the result of these operations is always an integer.
- Integers are not closed under division, as the result of dividing one integer by another may be a non-integer.
Types of Integers
- Positive integers: 1, 2, 3, ... (also known as natural numbers)
- Negative integers: ..., -3, -2, -1
- Non-positive integers: 0, -1, -2, -3, ... (including zero and negative integers)
Operations on Integers
- Addition: The sum of two integers is always an integer.
- Subtraction: The difference of two integers is always an integer.
- Multiplication: The product of two integers is always an integer.
- Division: The quotient of two integers is not always an integer.
Notation
- Integers are often denoted using the symbol "Z" (from the German word "Zahlen", meaning "numbers").
- For example, the set of integers is represented as ℤ.
Definition of Integers
- Integers are whole numbers, either positive, negative, or zero, without a fractional part.
- The set of integers includes {..., -3, -2, -1, 0, 1, 2, 3,...}.
Properties of Integers
- Integers are closed under addition, meaning the result of adding two integers is always an integer.
- Integers are closed under subtraction, meaning the result of subtracting one integer from another is always an integer.
- Integers are closed under multiplication, meaning the product of two integers is always an integer.
- Integers are not closed under division, meaning the result of dividing one integer by another may not be an integer.
Classification of Integers
- Positive integers are 1, 2, 3,... (also known as natural numbers).
- Negative integers are ..., -3, -2, -1.
- Non-positive integers include 0, -1, -2, -3,... (including zero and negative integers).
Operations on Integers
- The sum of two integers is always an integer, using addition.
- The difference of two integers is always an integer, using subtraction.
- The product of two integers is always an integer, using multiplication.
- The quotient of two integers is not always an integer, using division.
Notation for Integers
- Integers are often denoted using the symbol "Z" (from the German word "Zahlen", meaning "numbers").
- The set of integers is represented as ℤ.
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Description
Learn about the definition and properties of integers, including types of integers and their behavior under various operations.
