Definition:Ordered Pair/Notation

Definition

In the field of symbolic logic and modern treatments of set theory, the notation $\sequence {a, b}$ is often seen to denote an ordered pair.

In sources where the possibility of confusion is only minor, one can encounter $a \times b$ for $\tuple {a, b}$ on an ad hoc basis.

These notations are not used on $\mathsf{Pr} \infty \mathsf{fWiki}$, where $\tuple {a, b}$ is used exclusively.

Sources

• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $1$: Pairs, Relations, and Functions

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• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Relations
• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 2$: The Axioms of Group Theory (Footnote $*$)
• 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 2.1$: Sets: Exercise $\text{C}$
• 1965: Claude Berge and A. Ghouila-Houri: Programming, Games and Transportation Networks ... (previous) ... (next): $1$. Preliminary ideas; sets, vector spaces: $1.1$. Sets
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.2$. Sets
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ordered pair
• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 4$ The pairing axiom: Ordered Pairs