Definition:Uncountable/Set

Definition

A set which is infinite but not countable is described as uncountable.

Also known as

An uncountable collection can also be seen as:

non-denumerable or nondenumerable

non-countable.

Also see

• Definition:Finite Set
• Definition:Infinite Set
• Definition:Countable Set
• Definition:Countably Infinite Set

• Sufficient Conditions for Uncountability

• Results about uncountable sets can be found here.

Sources

• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 2.2$: Countable sets
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Mappings: $\S 15$
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Point Sets: $15.$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): nondenumerable
• 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 7$: Countable and Uncountable Sets
• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $2.4$
• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Cantor's Theorem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): nondenumerable
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 2$ Countable or uncountable?
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): Appendix $\text{A}.5$: Definition $\text{A}.25$