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Results tagged with real-analysis
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user 1708
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
6
votes
1
answer
183
views
Reference request: A collection of topologies on $\mathbb{N}$ formed via series
First, some quick notation: for any series $\sum_{n=1}^\infty a_n$ whose terms are positive real numbers, and for any subset $M = \{m_1, m_2,...\} \subseteq \mathbb{N}$, we write $\sum_M a_n$ to mean …
- 6,546
9
votes
Accepted
Cardinality of Equivalence Classes of Cauchy Sequences
It's the same as the size of the real numbers. Here's a rough sketch of the proof.
For each element of (0,1) (which has the same cardinality as the reals), I'm going to construct a distinct sequence …
- 6,546