set
collection of objects; unordered, may repeat
element
object in a set
roster notation
{}
empty set
set with no elements
set of natural numbers
N; all numbers >= 0
set of all integers
Z
set of rational numbers
Q; set of numbers that can be expressed as a/b where b != 0
set of irrational numbers
P
set of real numbers
R
A = { x -> S : P(x)}
A is defined as all x in S such that P(x)
universal set
elements mentioned in a particular context, even if those elements are outside of A or B
subset
every element in A is also an element of B, so A is a subset of B
proper subset
if A is a subset of B and there is x in B that is not in A, A is a proper subset of B
if the set {x, y} is within A, it is denoted as
{{x, y}}
cardinality
number of elements in a set
power set
a set with elements that are all possible subsets of A;
|P(A)| = 2^(|A|)
cardinality of a power set
if |A| = n, |P(A)| = 2^n
A union B
either A or B
A intersect B
A and B; shared
indicing
symmetric difference (A ⊖ B)
In A or B, but not both
difference (A - B)
In A but not B
complement
not in A; in all other sets and/or universal set
Cartesian Product
denoted A x B;
the set of all ordered pairs in which the first entry is in A and the second is in B
