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Questions and Answers
What is the set of integers denoted by?
What is the set of integers denoted by?
Which property states that the order of integers in an operation does not change the result?
Which property states that the order of integers in an operation does not change the result?
What is the result of dividing one integer by another?
What is the result of dividing one integer by another?
What is the distance of an integer from zero?
What is the distance of an integer from zero?
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What is the integer with the same magnitude but opposite sign?
What is the integer with the same magnitude but opposite sign?
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What is the multiplicative inverse of an integer, except for zero?
What is the multiplicative inverse of an integer, except for zero?
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What is the result of adding or multiplying two integers?
What is the result of adding or multiplying two integers?
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What is the additive identity, which is neither positive nor negative?
What is the additive identity, which is neither positive nor negative?
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Study Notes
Definition of Integers
- Integers are whole numbers, either positive, negative, or zero, without a fractional part.
- They are denoted by the symbol "Z" and include the set of numbers {..., -3, -2, -1, 0, 1, 2, 3, ...}.
Properties of Integers
- Closure: The result of adding or multiplying two integers is always an integer.
- Commutative Property: The order of integers in an operation does not change the result. (e.g., a + b = b + a, a × b = b × a)
- Associative Property: The order in which integers are grouped in an operation does not change the result. (e.g., (a + b) + c = a + (b + c), (a × b) × c = a × (b × c))
- Distributive Property: Integers can be distributed across addition and subtraction operations. (e.g., a × (b + c) = a × b + a × c)
Types of Integers
- Positive Integers: Integers greater than zero (e.g., 1, 2, 3, ...).
- Negative Integers: Integers less than zero (e.g., -1, -2, -3, ...).
- Zero: The additive identity, which is neither positive nor negative.
Operations on Integers
- Addition: The result of adding two integers is always an integer.
- Subtraction: The result of subtracting one integer from another is always an integer.
- Multiplication: The result of multiplying two integers is always an integer.
- Division: The result of dividing one integer by another is not always an integer, but may be a fraction or a decimal.
Important Concepts
- Absolute Value: The distance of an integer from zero, always a positive value.
- Opposite: The integer with the same magnitude but opposite sign.
- Reciprocal: The multiplicative inverse of an integer, except for zero.
Definition and Properties of Integers
- Integers are whole numbers, either positive, negative, or zero, without a fractional part, denoted by the symbol "Z".
- The set of integers includes {..., -3, -2, -1, 0, 1, 2, 3,...}.
- Integers exhibit closure under addition and multiplication.
- Integers follow the commutative property of addition and multiplication.
- Integers follow the associative property of addition and multiplication.
- Integers follow the distributive property across addition and subtraction.
Types of Integers
- Positive integers are integers greater than zero (e.g., 1, 2, 3,...).
- Negative integers are integers less than zero (e.g., -1, -2, -3,...).
- Zero is the additive identity, neither positive nor negative.
Operations on Integers
- The result of adding two integers is always an integer.
- The result of subtracting one integer from another is always an integer.
- The result of multiplying two integers is always an integer.
- The result of dividing one integer by another is not always an integer, but may be a fraction or a decimal.
Important Concepts
- The absolute value of an integer is its distance from zero, always a positive value.
- The opposite of an integer has the same magnitude but opposite sign.
- The reciprocal of an integer is its multiplicative inverse, except for zero.
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Description
Learn about the definition and properties of integers, including closure, commutative property, and associative property. Test your understanding of whole numbers!
