Difference between revisions of "Ordered pair"
From Encyclopedia of Mathematics
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Given sets $A$ and $B$ the set of all ordered pairs $(a,b)$ with $a \in A$ and $b \in B$ is the [[Cartesian product]] $A \times B$. | Given sets $A$ and $B$ the set of all ordered pairs $(a,b)$ with $a \in A$ and $b \in B$ is the [[Cartesian product]] $A \times B$. | ||
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| + | Compare with [[unordered pair]]. | ||
====References==== | ====References==== | ||
* P. R. Halmos, ''Naive Set Theory'', Undergraduate Texts in Mathematics, Springer (1960) ISBN 0-387-90092-6 | * P. R. Halmos, ''Naive Set Theory'', Undergraduate Texts in Mathematics, Springer (1960) ISBN 0-387-90092-6 | ||
Revision as of 21:19, 5 December 2014
2020 Mathematics Subject Classification: Primary: 03E [MSN][ZBL]
A construct $(a,b)$ of two objects $a$ and $b$ in which order is significant; $(a,b)$ is not the same as $(b,a)$ unless $a=b$. Equality between ordered pairs is defined by $$ (a,b) = (c,d) \ \Leftrightarrow \ a=c \wedge b=d \ . $$
A realisation in terms of axiomatic set theory is to write $$ (a,b) = \{ \{a\} , \{a,b\} \} \ . $$
Given sets $A$ and $B$ the set of all ordered pairs $(a,b)$ with $a \in A$ and $b \in B$ is the Cartesian product $A \times B$.
Compare with unordered pair.
References
- P. R. Halmos, Naive Set Theory, Undergraduate Texts in Mathematics, Springer (1960) ISBN 0-387-90092-6
How to Cite This Entry:
Ordered pair. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ordered_pair&oldid=34778
Ordered pair. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ordered_pair&oldid=34778