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cauchy_sequence [2014/01/30 21:24] nikolaj |
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| ===== Cauchy sequence ===== | ===== Cauchy sequence ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $\langle X,d\rangle$ $\dots$ Metric space | | + | | @#55CCEE: context | @#55CCEE: $\langle X,d\rangle$ $\dots$ Metric space | |
| - | | @#FFBB00: $x\in \text{CauchySeq}(X) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $x\in \text{CauchySeq}(X) $ | |
| - | | @#88DDEE: $x\in \text{InfSequence}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $x\in \text{InfSequence}(X) $ | |
| - | | @#DDDDDD: $\varepsilon\in \mathbb R,\ \varepsilon>0$ | | + | | @#DDDDDD: range | @#DDDDDD: $\varepsilon\in \mathbb R,\ \varepsilon>0$ | |
| - | | @#DDDDDD: $n,m,N\in\mathbb N$ | | + | | @#DDDDDD: range | @#DDDDDD: $n,m,N\in\mathbb N$ | |
| - | | @#55EE55: $\forall\varepsilon.\ \exists N.\ \forall (n,m>N).\ d(x_n,x_m)<\varepsilon$ | | + | | @#55EE55: postulate | @#55EE55: $\forall\varepsilon.\ \exists N.\ \forall (n,m>N).\ d(x_n,x_m)<\varepsilon$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| Wikipedia: [[http://en.wikipedia.org/wiki/Cauchy_sequence|Cauchy sequence]] | Wikipedia: [[http://en.wikipedia.org/wiki/Cauchy_sequence|Cauchy sequence]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Metric space]] | [[Metric space]] | ||
| - | === Refinement of === | + | === Related === |
| [[Infinite sequence]] | [[Infinite sequence]] | ||
