Definition:Ordered Tuple as Ordered Set/Ordered Quadruple
< Definition:Ordered Tuple as Ordered Set(Redirected from Definition:Ordered Quadruple)
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Definition
The ordered quadruple $\tuple {a, b, c, d}$ of elements $a$, $b$, $c$ and $d$ is defined either as the ordered pair:
- $\tuple {a, \tuple {b, c, d} }$
or:
- $\tuple {\tuple {a, b, c}, d}$
where $\tuple {a, b, c}$ and $\tuple {b, c, d}$ are themselves ordered triples.
Whichever definition is chosen does not matter much, as long as it is understood which is used. And even then, the importance is limited.
Sources
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Graphs and functions
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Ordered Pairs
- 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: $n$-tuples
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): quadruple