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1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeAug 22nd 2012
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   Author: TobyBartels
   Format: MarkdownItexAnother new article: [[sequence space]]. I await the inevitable report that this term is also used for other things.

   Another new article: sequence space. I await the inevitable report that this term is also used for other things.

2. • CommentRowNumber2.
   • CommentAuthorMark Meckes
   • CommentTimeAug 28th 2012
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   Author: Mark Meckes
   Format: MarkdownItexYou certainly use the term in the way I expected, but I take issue with the statement "The name ‘sequence space’ is not often encountered". Personally, I encounter that name all the time

   You certainly use the term in the way I expected, but I take issue with the statement “The name ‘sequence space’ is not often encountered”. Personally, I encounter that name all the time

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2012
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   Author: Urs
   Format: MarkdownItexI have added a link to the entry from the "Important subclasses"-section at _[[topological vector space]]_, but probably this deserves to be listed more systematically. Somehow.

   I have added a link to the entry from the “Important subclasses”-section at topological vector space, but probably this deserves to be listed more systematically. Somehow.

4. • CommentRowNumber4.
   • CommentAuthorTom Leinster
   • CommentTimeAug 28th 2012
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   Author: Tom Leinster
   Format: MarkdownItexI added the synonym $c_{00}$ for $c_c$. I entirely don't get the point about $\ell^\infty$ versus $c_b$. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says "two different ways of thinking about the same thing", but I see literally no difference apart from the change of name.

   I added the synonym $c_{00}$ for $c_c$.

   I entirely don’t get the point about $\ell^\infty$ versus $c_b$. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says “two different ways of thinking about the same thing”, but I see literally no difference apart from the change of name.

5. • CommentRowNumber5.
   • CommentAuthorTobyBartels
   • CommentTimeAug 28th 2012
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   Author: TobyBartels
   Format: MarkdownItex>Personally, I encounter that name all the time Good, maybe it is not such an obscure name, just left out of my education. >I entirely don't get the point about $\ell^\infty$ versus $c_b$. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says "two different ways of thinking about the same thing", but I see literally no difference apart from the change of name. One way is as the culmination of the sequence $(l^p)_{0 \lt p \lt \infty}$, the other way is as the culmination of the sequence $(c_c, c_0, c_\infty)$. Note that when we generalise $N$ from a set to a non-discrete space (and start using capital letters for some reason), the two notions diverge. (I'll add something about this to the article.)

   Personally, I encounter that name all the time

   Good, maybe it is not such an obscure name, just left out of my education.

   I entirely don’t get the point about $\ell^\infty$ versus $c_b$. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says “two different ways of thinking about the same thing”, but I see literally no difference apart from the change of name.

   One way is as the culmination of the sequence $(l^p)_{0 \lt p \lt \infty}$, the other way is as the culmination of the sequence $(c_c, c_0, c_\infty)$. Note that when we generalise $N$ from a set to a non-discrete space (and start using capital letters for some reason), the two notions diverge. (I’ll add something about this to the article.)

6. • CommentRowNumber6.
   • CommentAuthorMark Meckes
   • CommentTimeAug 28th 2012
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   Author: Mark Meckes
   Format: MarkdownItexTo paraphrase something I once heard in a talk, the name "sequences spaces" is well-known, in the usual sense of "well-known among those who know it well".

   To paraphrase something I once heard in a talk, the name “sequences spaces” is well-known, in the usual sense of “well-known among those who know it well”.

7. • CommentRowNumber7.
   • CommentAuthorTom Leinster
   • CommentTimeAug 29th 2012
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   Author: Tom Leinster
   Format: MarkdownItexThanks for the clarification, Toby. I sort of see the point, but the trouble is that I don't see in any *precise* sense what progression is happening in the sequence $(c_c, c_0, c_\infty, c_b)$. So what you've written is almost as mysterious to me as if it had been the following: > We write $\mathbf{A}$ for the category of **abelian** groups: $x y = y x$ for all $x$ and $y$. [...] We write $\mathbf{B}$ for the category of **abelian** groups: $x y = y x$ for all $x$ and $y$. Indeed, $\mathbf{A} = \mathbf{B}$, two different ways of thinking about the same thing. (But they generalise differently.)

   Thanks for the clarification, Toby. I sort of see the point, but the trouble is that I don’t see in any precise sense what progression is happening in the sequence $(c_c, c_0, c_\infty, c_b)$. So what you’ve written is almost as mysterious to me as if it had been the following:

   We write $\mathbf{A}$ for the category of abelian groups: $x y = y x$ for all $x$ and $y$. […] We write $\mathbf{B}$ for the category of abelian groups: $x y = y x$ for all $x$ and $y$. Indeed, $\mathbf{A} = \mathbf{B}$, two different ways of thinking about the same thing. (But they generalise differently.)

8. • CommentRowNumber8.
   • CommentAuthorTobyBartels
   • CommentTimeAug 29th 2012
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   Author: TobyBartels
   Format: MarkdownItexWould that make more sense if, later in the article, there was a section on generalisations where they did indeed generalise differently?

   Would that make more sense if, later in the article, there was a section on generalisations where they did indeed generalise differently?

9. • CommentRowNumber9.
   • CommentAuthorTom Leinster
   • CommentTimeAug 30th 2012
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   Author: Tom Leinster
   Format: MarkdownItexNot sure. It's probably best to just ignore me and carry on. It was only a niggle anyway.

   Not sure. It’s probably best to just ignore me and carry on. It was only a niggle anyway.