Chapter 0.3: Sets Flashcards
(41 cards)
What is a set?
An unordered collection of unique objects.
What kind of values can a set have?
Any kind of value.
Why is set Notation helpful?
Makes writing sets less verbose
How does A = {1,2,3} read?
“A is the set containing the elements 1, 2, and 3.”
How does a ∈ {a,b,c} read? ∉?
“a is an element of the set containing the letters a, b, and c.
A = {1,b,{x, y, z}, ∅}, B = {1,b} and C = {x,y,z}. is B a subset of A? is C a subset of A?
Yes, No
What are curly braces used for?
Enclosing the elements of a set
What is ℕ?
Natural numbers set, not everyone includes 0, but the textbook does.
What does “:” read? do?
“such that”
Separates the elements in the set from the conditions to be satisfied.
How is this read: A = {x ∈ ℕ : ∃n ∈ ℕ(x = 2n) }? Can this be read more concisely?
“the set of all x in the natural numbers, such that there exists some n in the natural numbers for which x is twice n.”
“the set of all natural numbers that are even”
What are substitute symbols for ∈ that mathematicians like to use?
“|” instead of “:”
What is set builder notation?
Set building instructions that require a condition that elements must satisfy for inclusion
In set builder notation, the ____ sometimes comes before the “:”.
Condition
What is this symbol? ∅
the empty set is the set which contains no elements. Is a subset of every set
What is this symbol? 𝓤
the universe set is the set of all elements
What is this symbol? ℚ
the set of rational numbers
What is this symbol? ℤ
the set of all integers {…, -3, -2, -1, 0, 1, 2, 3, …}
What is this symbol? ℝ
the set of all real numbers. Any number that is rational or irrational
What is this symbol? ℕ
the set of all natural numbers {0, 1, 2, 3, …}
What is this symbol? P(A)
the power set of any set A that is the set of all subsets of A
Read: {1,2,3}
The set containing the elements 1, 2, and 3.
read: { x : x > 2 }
“x is the set of all x such that x is greater than 2”
What is this symbol? ⊆
“Subet of”. A ⊆ B asserts that A is a subset of B: every element of A is also an element of B
What is this symbol? ⊂
“Proper subset of”. A ⊂ B asserts that A is a proper subset of B: every element of A is also an element of B but A does not equal b
