Definition:Set/Also known as

Set: Also known as

In the original translation by Jourdain of Georg Cantor's original work, this concept was called an aggregate. The term can be seen in subsequent works, but has now mostly been superseded by the term set.

Sometimes the terms class, family, system or collection are used. In some contexts, the term space is used. However, beware that these terms are usually used for more specific things than just as a synonym for set.

On this website, the terms class, family and space are not used as synonyms for set, being reserved specifically for the concepts to which they apply.

Sources

• 1915: Georg Cantor: Contributions to the Founding of the Theory of Transfinite Numbers ... (previous) ... (next): First Article: $\S 1$: The Conception of Power or Cardinal Number: $(1)$
• 1939: E.G. Phillips: A Course of Analysis (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.2$ Fundamental notions
• 1951: J.C. Burkill: The Lebesgue Integral ... (previous) ... (next): Chapter $\text {I}$: Sets of Points: footnote $\dagger$
• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Introduction $\S 1$: Operations on Sets
• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Preliminaries: Sets: footnote ${}*$
• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 1$: The Axiom of Extension
• 1961: John G. Hocking and Gail S. Young: Topology ... (previous) ... (next): A Note on Set-Theoretic Concepts
• 1963: George F. Simmons: Introduction to Topology and Modern Analysis ... (previous) ... (next): $\S 1$: Sets and Set Inclusion
• 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): Chapter $1$: A Common Language: $\S 1.1$ Sets
• 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Introduction: Set-Theoretic Notation
• 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $1$ Set Theory: $1$. Sets and Functions: $1.1$: Basic definitions
• 1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras
• 1972: Patrick Suppes: Axiomatic Set Theory (2nd ed.) ... (previous) ... (next): $\S 1.1$ Set Theory and the Foundations of Mathematics: Footnote ${}*$
• 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $1$: Numbers: Sets
• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{III}$: The Logic of Predicates $(1): \ 3$: Quantifiers
• 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.1$: What is a Set?
• 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $2$. Graphs: Sets
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): Appendix $\text A$: Sets and Functions: $\text{A}.1$: Sets
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): class
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): class
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 6$ Significance of the results