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Both sides previous revision Previous revision Next revision | Previous revision | ||
metric [2013/09/13 17:38] nikolaj |
metric [2014/11/20 13:00] nikolaj |
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===== Metric ===== | ===== Metric ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $ X $ | | + | | @#55CCEE: context | @#55CCEE: $ X $ ... set | |
- | + | | @#FFBB00: definiendum | @#FFBB00: $d\in$ it | | |
- | | @#FFBB00: $d\in \text{Metric}(X)$ | | + | | @#55EE55: postulate | @#55EE55: $d:X\times X \to \mathbb{R}_+$ | |
- | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)=0 \implies x=y$ | | |
- | | @#55EE55: $d:X\times X \to \mathbb{R}_+$ | | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)=d(y,x)$ | |
- | + | | @#55EE55: postulate | @#55EE55: $ d(x,y)\le d(x,p)+d(p,y)$ | | |
- | | @#55EE55: $ d(x,y)=0 \implies x=y$ | | + | |
- | | @#55EE55: $ d(x,y)=d(y,x)$ | | + | |
- | | @#55EE55: $ d(x,y)\le d(x,p)+d(p,y)$ | | + | |
==== Discussion ==== | ==== Discussion ==== | ||
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=== Equivalent to === | === Equivalent to === | ||
[[Metric space]] | [[Metric space]] | ||
- | === Requirements === | + | === Context === |
[[Non-negative real number]] | [[Non-negative real number]] | ||