Denoting Sets
Sets are defined using the description or roster methods. The objects in a set are called members or elements of the set.
The cardinality of a set is the number of elements in a set.
Two sets are equal if they contain the same number.
Two sets are equivalent if they have the same number of elements.
Sets of Numbers
Natural Numbers: {1, 2, 3, ... }
Whole Numbers: {0, 1, 2, 3, ... }
Integers: {...,, -2, -1, 0, 1, 2, ... }
Rational Numbers: {a/b where a is an integer and b a nonzero integer}
Special Sets
The universal set contains all the elments under consideration in a given discussion.
The empty set contains no elements.
Venn Diagrams
One set divides the universe into 2 regions.
Two sets divide the universe into 4 regions.
Three sets divide the universe into 8 regions.
Complement
The complement of a set S is consists of everything that is not in S.
Subsets
A set A is a subset of a set B, if every element of A is also an element of B.
A set A is a proper subset of a set B, if every element of A
is also an element of B and A and B are not equal sets.