Definition:Relative Complement/Also known as
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Relative Complement: Also known as
Some authors refer to the relative complement as just the (set) complement, and use the term relative complement for the set difference $S \setminus T$ when the stipulation $T \subseteq S$ is not required.
Others emphasize the connection with set difference by referring to the relative complement as a proper difference.
Thus, in this view, the relative complement is a specific case of a set difference.
Sources
- 1951: J.C. Burkill: The Lebesgue Integral ... (previous) ... (next): Chapter $\text {I}$: Sets of Points: $1 \cdot 1$. The algebra of sets
- 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 5$: Complements and Powers
- 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
- 1965: A.M. Arthurs: Probability Theory ... (previous) ... (next): Chapter $1$: Set Theory: $1.3$: Set operations
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 3$: Unions and Intersections of Sets
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Sets
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 6$: Subsets