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cauchy_sequence [2014/01/30 21:37] nikolaj |
cauchy_sequence [2014/03/24 19:38] 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]] | ||
- | === Related === | + | === Requirements === |
[[Infinite sequence]] | [[Infinite sequence]] |