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ordered_pair [2013/09/06 21:49] nikolaj |
ordered_pair [2014/12/08 10:15] nikolaj |
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===== Ordered pair ===== | ===== Ordered pair ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $ X,Y $ | | + | | @#55CCEE: context | @#55CCEE: $ X,Y $ | |
- | | @#FFBB00: $ \langle X,Y \rangle \equiv \{\{X\},\{X,Y\}\} $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle X,Y \rangle \equiv \{\{X\},\{X,Y\}\} $ | |
==== Discussion ==== | ==== Discussion ==== | ||
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This induces the n'th projection $\pi_n$ alla $\pi_3(\langle x_1,x_2,x_3,x_4,x_5\rangle)=\pi_2(\pi_1(\pi_1(\langle x_1,x_2,x_3,x_4,x_5\rangle)))$. | This induces the n'th projection $\pi_n$ alla $\pi_3(\langle x_1,x_2,x_3,x_4,x_5\rangle)=\pi_2(\pi_1(\pi_1(\langle x_1,x_2,x_3,x_4,x_5\rangle)))$. | ||
+ | |||
+ | === For non-negative integers === | ||
+ | There are bijections between $\mathbb N$ and ${\mathbb N}^2$ and so one can encode pairs of numbers as numbers. | ||
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Ordered_pair|Ordered pair]] | Wikipedia: [[http://en.wikipedia.org/wiki/Ordered_pair|Ordered pair]] | ||
==== Parents ==== | ==== Parents ==== | ||
- | === Requirements === | + | === Context === |
[[Unordered pair]] | [[Unordered pair]] | ||