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# Properties of Integers

Created by
@SaneEarth

### What is an integer?

A whole number, either positive, negative, or zero, without a fractional part.

Division

Natural numbers

### What is the set of integers represented as?

<p>ℤ</p> Signup and view all the answers

### What is the result of the addition of two integers?

<p>An integer</p> Signup and view all the answers

### What is a non-positive integer?

<p>0, -1, -2, -3,...</p> Signup and view all the answers

## 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.

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