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infinite_series [2013/09/07 19:28] nikolaj |
infinite_series [2014/03/21 11:11] 127.0.0.1 external edit |
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| ===== Infinite series ===== | ===== Infinite series ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $M$ ... monoid, metric space | | + | | @#55CCEE: context | @#55CCEE: $M$ ... monoid, metric space | |
| - | | @#88DDEE: $ S \in \mathrm{Sequence}(M)$ | | + | | @#55CCEE: context | @#55CCEE: $ S \in \mathrm{InfSequence}(M)$ | |
| - | | @#FFBB00: $\sum_{k=1}^\infty S_k\equiv \mathrm{lim}_{n\to\infty}\sum_{k=1}^n S_k$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\sum_{k=1}^\infty S_k\equiv \mathrm{lim}_{n\to\infty}\sum_{k=1}^n S_k$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| === Element of === | === Element of === | ||
| [[Monoid]] | [[Monoid]] | ||
| - | === Requirements === | + | === Context === |
| [[Finite sum over a monoid]], [[Limit in a metric space]] | [[Finite sum over a monoid]], [[Limit in a metric space]] | ||
