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Questions and Answers
What is the set of numbers that includes all positive integers?
What is the set of numbers that includes all positive integers?
Which property states that a + b = b + a?
Which property states that a + b = b + a?
What is the set of numbers that includes all real and imaginary numbers?
What is the set of numbers that includes all real and imaginary numbers?
What is the number that, when added to any number, does not change its value?
What is the number that, when added to any number, does not change its value?
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Which property states that a × (b + c) = a × b + a × c?
Which property states that a × (b + c) = a × b + a × c?
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What is the set of numbers that includes fractions and can be expressed as a finite decimal?
What is the set of numbers that includes fractions and can be expressed as a finite decimal?
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Study Notes
Classification of Numbers
- Natural Numbers: 1, 2, 3, ... (positive integers)
- Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
- Rational Numbers: fractions, e.g. 3/4, 22/7, can be expressed as a finite decimal
- Irrational Numbers: cannot be expressed as a finite decimal, e.g. π, e, sqrt(2)
- Real Numbers: includes rational and irrational numbers
- Complex Numbers: includes real and imaginary numbers, e.g. 3 + 4i
Properties of Numbers
- Commutative Property: a + b = b + a, a × b = b × a
- Associative Property: (a + b) + c = a + (b + c), (a × b) × c = a × (b × c)
- Distributive Property: a × (b + c) = a × b + a × c
- Additive Identity: 0, when added to any number, does not change its value
- Multiplicative Identity: 1, when multiplied to any number, does not change its value
- Additive Inverse: for each number a, there exists -a, such that a + (-a) = 0
- Multiplicative Inverse: for each number a, there exists 1/a, such that a × (1/a) = 1
Classification of Numbers
- Natural numbers are positive integers, starting from 1 and going upwards (1, 2, 3,...).
- Whole numbers include natural numbers and 0, representing non-negative integers (0, 1, 2, 3,...).
- Integers encompass both positive and negative whole numbers (...,-3, -2, -1, 0, 1, 2, 3,...).
- Rational numbers consist of fractions that can be expressed as finite decimals (e.g., 3/4, 22/7).
- Irrational numbers cannot be expressed as finite decimals and include numbers like π, e, and sqrt(2).
- Real numbers comprise both rational and irrational numbers.
- Complex numbers combine real and imaginary numbers, such as 3 + 4i.
Properties of Numbers
- The commutative property allows for swapping numbers during addition and multiplication: a + b = b + a, a × b = b × a.
- The associative property enables rearranging numbers during addition and multiplication: (a + b) + c = a + (b + c), (a × b) × c = a × (b × c).
- The distributive property facilitates expanding a single operation across multiple terms: a × (b + c) = a × b + a × c.
- The additive identity, 0, maintains a number's value when added to it.
- The multiplicative identity, 1, preserves a number's value when multiplied by it.
- Each number has an additive inverse (-a) that results in 0 when added together: a + (-a) = 0.
- Each number has a multiplicative inverse (1/a) that equals 1 when multiplied together: a × (1/a) = 1.
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Description
Quiz about different types of numbers, including natural, whole, integers, rational, irrational, real, and complex numbers
