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explicitly states that conditional convergence is the exact opposite of unconditional convergence. That is, the given series converges, but there exist reorderings of the series which diverge or converge to a different limit. The corresponding article on conditional convergence in the German
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wikipedia goes in the same line. Conditional convergence ist not always equivalent to non-absolute convergence, e.g. in infinite-dimensional Banach spaces.
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is a big issue and should be mentioned or even be explained on this page. The best reference is probably
Boardman's famous article
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I glanced around, I could not find anywhere the above definition in Rudin's book. Another problem. I would imagine that
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I have some problems with this definition. Rudin's book is the only reference in this page. In 3.46 Rudin says:
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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This is really weird. I think that this page should be investigated and possibly changed.
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that reports a definition similar to the above; but it cites the book
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and (searching in the above link) that book never uses the word
368:{\displaystyle \scriptstyle \sum \limits _{n=0}^{\infty }a_{n}}
258:{\displaystyle \scriptstyle \sum \limits _{n=0}^{\infty }a_{n}}
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The definition on top of this web page currently says:
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