Integers Definition and Properties

Definition and Properties

• An integer is a whole number, either positive, negative, or zero, without a fractional part.
• Integers are denoted by the symbol "Z" and include the set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
• Integers can be represented on the number line, with positive integers to the right of zero and negative integers to the left of zero.

Types of Integers

• Positive integers: integers greater than zero, denoted by Z+ (e.g., 1, 2, 3, ...).
• Negative integers: integers less than zero, denoted by Z- (e.g., -1, -2, -3, ...).
• Non-positive integers: integers less than or equal to zero, denoted by Z0- (e.g., 0, -1, -2, ...).
• Non-negative integers: integers greater than or equal to zero, denoted by Z0+ (e.g., 0, 1, 2, ...).

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, but may be a fraction or a decimal.

Important Concepts

• Even integers: integers that are divisible by 2, denoted by 2Z (e.g., ..., -4, -2, 0, 2, 4, ...).
• Odd integers: integers that are not divisible by 2, denoted by 2Z + 1 (e.g., ..., -3, -1, 1, 3, ...).
• Prime integers: integers greater than 1 that have only two factors: 1 and themselves (e.g., 2, 3, 5, 7, ...).
• Composite integers: integers greater than 1 that have more than two factors (e.g., 4, 6, 8, 9, ...).

Definition and Properties of Integers

• An integer is a whole number with no fractional part, either positive, negative, or zero.
• Integers are denoted by the symbol "Z" and include {..., -3, -2, -1, 0, 1, 2, 3,...}.
• Integers can be represented on the number line, with positive integers to the right of zero and negative integers to the left.

Types of Integers

• Positive integers are integers greater than zero, denoted by Z+ (e.g., 1, 2, 3,...).
• Negative integers are integers less than zero, denoted by Z- (e.g., -1, -2, -3,...).
• Non-positive integers are integers less than or equal to zero, denoted by Z0- (e.g., 0, -1, -2,...).
• Non-negative integers are integers greater than or equal to zero, denoted by Z0+ (e.g., 0, 1, 2,...).

Operations on Integers

• The sum of two integers is always an integer (addition).
• The difference of two integers is always an integer (subtraction).
• The product of two integers is always an integer (multiplication).
• The quotient of two integers is not always an integer, but may be a fraction or a decimal (division).

Important Concepts

• Even integers are integers divisible by 2, denoted by 2Z (e.g., ..., -4, -2, 0, 2, 4,...).
• Odd integers are integers not divisible by 2, denoted by 2Z + 1 (e.g., ..., -3, -1, 1, 3,...).
• Prime integers are integers greater than 1 with only two factors: 1 and themselves (e.g., 2, 3, 5, 7,...).
• Composite integers are integers greater than 1 with more than two factors (e.g., 4, 6, 8, 9,...).

Learn about integers, including their definition, properties, and types. Discover how to represent integers on the number line and identify positive and negative integers.