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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
@@ Line 15: / Line 15: @@
 -----
 === 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 $
+$\sum_{k=1}^\infty a_n = y$
+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 $
 == Infinite sum ==