Subset                          A set that is part of a larger set.

Proper Set                     A proper subset of a set, denoted, is a subset that is strictly contained in and so necessarily excludes at least one member of. The empty set is therefore a proper subset of any nonempty set.

Equal Sets                     Sets that have exactly the same members. (Two words, plural)

Improper Subset              A subset that includes the entire parent set; see proper subset.

Empty Set                     In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.

Null Set                        A set that is empty; a set with no members.

Real Number                  Any rational or irrational number.

Infinite Set                    In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.

Natural Numbers             The number 1 and any other number obtained by adding 1 to it repeatedly.

Whole Numbers               A number without fractions; an integer.

Integers                        1. A whole number; a number that is not a fraction. 2. A thing complete in itself.

Rational Numbers              An integer or a fraction.

Irrational Numbers           A real number that cannot be expressed as a rational number.

Mutually Exclusive       Contradictory: unable to be both true at the same time.

by Kendall