Chapter 1: Sets Flashcards
vocab for ch1
set
a collection of objects
elements
aka members; objects that make up a set
empty set
aka null/void set; a set that contains no elements; denoted ∅
universal set
the largest set of elements being considered given a particular situation
set denoted by N
natural numbers {1, 2, 3, …}
set denoted by Z
integers {…-1, 0, 1,…}
set denoted by Q
rational numbers {m/n : m, n ∈ Z and n ≠ 0}
set denoted by C
complex numbers {a +bi : a, b ∈ R }
cardinality
the number of elements (not counting repitition) in the set; denoted by |A|
subset
X is a subset of Y if every element in X lies in Y
proper subset
X is a proper subset of Y if every element of X lies in Y and there is at least one element in Y that does not lie in X
power set
the set of all subset of A; denoted P(A)
intersection
the set of all the elements in set A that are also present in set B
union
a set containing all elements that are in A or in B (possibly both)
disjoint
if A ∩ B = ∅ ;when two sets have no elements in common; intersection of A and B is the null set
complement
every element in the universal set except those in A
difference
set of elements which belong to A but not to B
index set
given a collection of sets A1,…An, set I = {1, …, n}
pairwise disjoint
the collection S is pairwise disjoint if for every 2 distinct sets A, B ∈ S, A ∩ B = ∅
partition
a partition of Af can be defined as a collection of S of subsets of A satisfying 3 properties:
- X ≠ ∅ for every X ∈ S
- for every 2 sets X,Y ∈ S, either X=Y or X ∩ Y = ∅ (double check this condition)
- union of all elements equals set A
UX(subscript: X ∈ S) =A
Cartesian Product
given 2 sets A and B, cartesian product is defined as A x B = { (a, b) | a ∈ A, b ∈ B}
