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Questions and Answers
What is a subset of the set {George Bush, Toney Blair, Ronald Reagoan}?
What is a subset of the set {George Bush, Toney Blair, Ronald Reagoan}?
What is the definition of a subset?
What is the definition of a subset?
What is the term for numbers that can be expressed as a ratio of integers?
What is the term for numbers that can be expressed as a ratio of integers?
What is the set of numbers that includes the natural numbers, their negatives, and zero?
What is the set of numbers that includes the natural numbers, their negatives, and zero?
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What is the reason why 0 was not included in the natural numbers?
What is the reason why 0 was not included in the natural numbers?
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What is an example of a rational number that is not an integer?
What is an example of a rational number that is not an integer?
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Why are negative numbers considered an artificial construction?
Why are negative numbers considered an artificial construction?
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What is the relationship between integers and rational numbers?
What is the relationship between integers and rational numbers?
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What do the square brackets indicate in an interval?
What do the square brackets indicate in an interval?
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What does the symbol +∞ represent in an interval?
What does the symbol +∞ represent in an interval?
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What is an interval that has finite real numbers as end points called?
What is an interval that has finite real numbers as end points called?
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What is the characteristic of an interval of the form [a, + ∞)?
What is the characteristic of an interval of the form [a, + ∞)?
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What do open dots represent in a geometric picture of an interval?
What do open dots represent in a geometric picture of an interval?
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What is the classification of an interval that goes on forever in either the positive or the negative directions?
What is the classification of an interval that goes on forever in either the positive or the negative directions?
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What is an interval that includes one endpoint but not the other called?
What is an interval that includes one endpoint but not the other called?
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What does the symbol −∞ represent in an interval?
What does the symbol −∞ represent in an interval?
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What does the symbol ∅ represent in set theory?
What does the symbol ∅ represent in set theory?
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What is the union of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
What is the union of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
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What does the notation A ⊂ B mean in set theory?
What does the notation A ⊂ B mean in set theory?
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What is the intersection of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
What is the intersection of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
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What does the notation a ∈ A mean in set theory?
What does the notation a ∈ A mean in set theory?
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What is the set-builder notation used for in set theory?
What is the set-builder notation used for in set theory?
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What does the notation A = B mean in set theory?
What does the notation A = B mean in set theory?
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What is the set of all positive integers less than 5, written in set notation?
What is the set of all positive integers less than 5, written in set notation?
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Study Notes
Sets
- A subset is a portion of a set A, where every member of B is also a member of A.
- A subset is denoted using curly brackets { }, e.g. {George Bush, Tony Blair} is a subset of {George Bush, Toney Blair, Ronald Reagoan}.
- Integers are a set of numbers including ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... .
Integers and Rational Numbers
- Integers are a subset of rational numbers.
- Rational numbers are formed by taking ratios of integers, e.g. 2/3, 7/5, 6/1, -5/2.
- Every integer is also a rational number, as an integer p can be written as a ratio p/1.
Intervals
- Intervals can extend indefinitely in either the positive or negative direction, or both.
- The symbols -∞ and +∞ do not represent numbers, but indicate that the interval extends indefinitely in the negative or positive direction, respectively.
- An interval that goes on forever in either direction is called an infinite interval.
- A finite interval has finite real numbers as end points, e.g. [a, b] or (a, b).
Set Notations
- a ∈ A means a is an element of the set A.
- a ∉ A means a is not an element of the set A.
- ∅ represents the empty set, or the set that contains nothing.
- A ∪ B represents the set of all elements of A and B taken together.
- A ∩ B represents the set of all elements that are in both A and B.
- A = B means A is exactly the same set as B.
- A ⊂ B means the set A is contained in the set B.
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Description
Quiz on understanding sets, subsets, and notation in mathematics. Learn about the concept of subset and its representation using curly brackets.
