24 Questions
What is a subset of the set {George Bush, Toney Blair, Ronald Reagoan}?
{George Bush, Tony Blair}
What is the definition of a subset?
A subset is a portion of a set where every member of the subset is also a member of the original set.
What is the term for numbers that can be expressed as a ratio of integers?
Rational Numbers
What is the set of numbers that includes the natural numbers, their negatives, and zero?
Integers
What is the reason why 0 was not included in the natural numbers?
It was considered a concept of the devil in ancient Greece
What is an example of a rational number that is not an integer?
2/3
Why are negative numbers considered an artificial construction?
They were developed to solve simple equations like x + 2 = 0
What is the relationship between integers and rational numbers?
Integers are a subset of rational numbers
What do the square brackets indicate in an interval?
That the end points are included in the interval
What does the symbol +∞ represent in an interval?
That the interval extends indefinitely in the positive direction
What is an interval that has finite real numbers as end points called?
A finite interval
What is the characteristic of an interval of the form [a, + ∞)?
It is closed
What do open dots represent in a geometric picture of an interval?
Endpoints that are not included in the interval
What is the classification of an interval that goes on forever in either the positive or the negative directions?
Infinite interval
What is an interval that includes one endpoint but not the other called?
Half-open interval
What does the symbol −∞ represent in an interval?
That the interval extends indefinitely in the negative direction
What does the symbol ∅ represent in set theory?
The empty set
What is the union of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
{1, 2, 3, 4, 5, 6, 7}
What does the notation A ⊂ B mean in set theory?
A is a subset of B
What is the intersection of sets A and B, if A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7}?
{1, 2, 3, 4}
What does the notation a ∈ A mean in set theory?
a is an element of the set A
What is the set-builder notation used for in set theory?
To specify the members of a set when it is inconvenient or impossible to list them
What does the notation A = B mean in set theory?
A is equal to B
What is the set of all positive integers less than 5, written in set notation?
{1, 2, 3, 4}
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.
Quiz on understanding sets, subsets, and notation in mathematics. Learn about the concept of subset and its representation using curly brackets.
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