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limit_in_a_metric_space [2015/06/25 21:29] nikolaj |
limit_in_a_metric_space [2015/11/26 22:28] nikolaj |
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| === Examples === | === Examples === | ||
| - | $ \forall (\varepsilon\in{\mathbb R}).\,\exists (m\in{\mathbb N}).\,\forall (n\ge_{\mathbb N} m).\,| \sum_{k=1}^n a_n - \sum_{k=1}^\infty a_n |<\varepsilon $ | + | $\sum_{k=1}^\infty = y$ |
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| + | means | ||
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| + | $ \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 $ | ||
| == Infinite sum == | == Infinite sum == | ||
