Questions and Answers
What is an integer?
A whole number, either positive, negative, or zero, without a fractional part.
What operation is not closure for integers?
Division
What is another term for positive integers?
Natural numbers
What is the set of integers represented as?
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What is the result of the addition of two integers?
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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.