Set (mathematics)

In logic and mathematics, a set is any collection of distinct elements.

Despite this intuitive definition, a set cannot be defined formally in terms of other mathematical objects, thus it is generally accepted that a set is an "undefined" entity. Because of this property, sets are fundamental structures in mathematics. Mathematicians have found ways to define many mathematical objects, such as the real numbers, in terms of sets.

Notation

Sets can be denoted by a list of objects separated with commas, enclosed with curly brackets. For example, {1, 2, 3} is the set of the numbers 1, 2, and 3. We say that 1, 2, and 3 are its members.

There are many other ways to write out sets. For example,

A = {x | 1 < x < 10, x is a natural number}

can be read as follows: A is the set of all x, where x is between 1 and 10, and x is a natural number. A could also be written as:

A = {2, 3, 4, 5, 6, 7, 8, 9}

See also

• Set theory
• Naive set theory
• Mathematics
• Aleph-0

• Cardinal number
• Transfinite algebra
• Continuum hypothesis
• Ernst Zermelo
• Thoralf Skolem
• Georg Cantor
• Zermelo-Fraenkel axioms
• Peano axioms