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limit_in_a_metric_space [2016/03/20 11:04] nikolaj |
limit_in_a_metric_space [2017/02/02 21:25] nikolaj |
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| === Examples === | === Examples === | ||
| - | $\sum_{k=1}^\infty a_n = y$ | + | $\sum_{k=1}^\infty a_k = y$ |
| means | means | ||
| - | $ \forall (\varepsilon\in{\mathbb R}_{>0}).\,\exists (m\in{\mathbb N}).\,\forall (n\ge_{\mathbb N} m).\,| \sum_{k=1}^n a_n - y \, |<\varepsilon $ | + | $ \forall (\varepsilon\in{\mathbb R}_{>0}).\,\exists (m\in{\mathbb N}).\,\forall (n\ge_{\mathbb N} m).\,| \sum_{k=1}^n a_k - y \, |<\varepsilon $ |
| == Infinite sum == | == Infinite sum == | ||
