Definition:Disjoint Sets

Definition

Two sets $S$ and $T$ are disjoint iff:

$S \cap T = \varnothing$

... that is, their intersection is the empty set - they have no elements in common.

Some early sources, for example Nathan Jacobson: Lectures in Abstract Algebra: I. Basic Concepts (1951), refer to such sets as non-overlapping.

Also see

• Pairwise disjoint

Sources

• Nathan Jacobson: Lectures in Abstract Algebra: I. Basic Concepts (1951): Introduction $\S 1$
• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 4$: Unions and Intersections
• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 1.3$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 3$
• George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$
• A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis (1968): $\S 1.2$
• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 5$
• T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 1$
• Gary Chartrand: Introductory Graph Theory (1977): Appendix $\text{A}.1$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 7$
• Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (1993): $\S 1.2$
• H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability (1996): Appendix $\text{A}.2$