Lesson 4: The Language of Sets

set

a collection of distinct objects

dinstinct

means no duplication of the object in the set (it is listed only once).

natural numbers

Counting numbers (also called positive integers)

integers

Naturals numbers, their negatives and 0

rational numbers

Numbers that can be represented as a/b, where a and b are integers and b≠0. The decimal representations are terminating or repeating

Irrational numbers

Numbers that cannot be expressed as the ratio of two integers. They are the non-repeating and non-terminating decimals.

real numbers

rational and irrational

Roster Method

The elements of a set are listed or enumerated in any order but no repetition and are enclosed by curly braces. (enumeration)

Set-builder Notation

The members of the set are defined by stating their common properties. (rule method)

Finite set

A set whose elements are limited or countable

Infinite Set

A set whose elements are unlimited or cannot be counted

Singleton Set

A set with only one element (unit set)

Null set

A set with no object or element (empty set)

Equal set

Two sets containing the same elements are equal

Equivalent set

If Sets A and B have the same number of
elements or the same cardinality, then they are equivalent sets

Cardinality

same number of elements

Disjoint Sets

Two sets with no common elements (non-intersection)

Subset

a set whose members are members of another set; a set contained within another set

2^n

subset formula

Proper subset

If every element of A is in B, but there is at least one element in B that is not in A

2^n - 1

proper subset formula

Superset

If A is a subset of B, then we can say that B is a ______ of A

Power sets

The set of all subsets of a set A

2^n

power set formula

Universal set

the set containing all the possible elements under consideration or the set containing all the elements of its subsets, without repetition

Complementary sets

if they have no common elements, and their union is the universal set.

Union

the set containing all the elements of both sets

Intersection

the set containing the common elements of both sets

Cross Product

the set of all ordered pairs (a, b), where the first element a is from set A, and the second element b is from set B