# Definition:Ordered Tuple as Ordered Set/Ordered Triple

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## Contents

## Definition

The **ordered triple** $\tuple {a, b, c}$ of elements $a$, $b$ and $c$ can be defined either as the ordered pair:

- $\tuple {a, \tuple {b, c} }$

or as the ordered pair:

- $\tuple {\tuple {a, b}, c}$

where $\tuple {a, b}$ and $\tuple {b, c}$ are themselves ordered pairs.

Whichever definition is chosen does not matter much, as long as it is understood which is used. And even then, the importance is limited.

## Also known as

An **ordered triple** is also sometimes seen named an **ordered triad**.

## Also see

## Sources

- 1964: W.E. Deskins:
*Abstract Algebra*... (previous) ... (next): $\S 1.2$: Definition $1.3$ - 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 $1$: Algebraic Structures: $\S 1$: The Language of Set Theory - 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 2$: Sets and functions: Graphs and functions - 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 3$. Ordered pairs; cartesian product sets - 2008: Paul Halmos and Steven Givant:
*Introduction to Boolean Algebras*... (previous) ... (next): Appendix $\text{A}$: Set Theory: Ordered Pairs