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The same content is present at nowhere dense but I felt this deserves a separate page. I'll be creating a page on Volterra's function in the near future if someone doesn't beat me to it  :-) - Gauge 06:07, 23 Aug 2004 (UTC)
There is a slight inconsistency here. Either the intervals removed at each step are the "middle quarter of the remaining intervals" or they are centred on a/2^n. But they cannot be both. The first leads to measure of 0.5, the second to measure of 0.53557368... -- Henrygb 17:17, 25 Apr 2005 (UTC)
Let the set be called S. By construction, S contains no intervals (i.e. S contains points that are seperate from each other.). And the measure of a single point is 0. So how can the total measure be 1/2? On the other hand, the total length of removal is 1/2, hence remaining length must be 1/2. Hence, S must contains intervals of length greater than 0. Can somebody please help me resolve this? 108.162.157.141 ( talk) 01:53, 28 November 2013 (UTC)
This article needs to explain the hausdorff dimension of the Generalized Cantor set, as listed on the wikipage List of fractals by Hausdorff dimension, which is shown as
Could someone report on whether the particular name Smith–Volterra–Cantor set is attested in the references, or at least in the wild? The basic underlying idea here (not necessarily the specific sequence using ) is pretty standard and will inevitably come up in almost any real analysis course when clarifying the distinction between measure and category. The specific name used here, on the other hand, I do not recall seeing outside Wikipedia.
I'm concerned that this name could have been what an editor thought the construction should be called, which is something we're not supposed to do, though that may not have been as clear in 2004 when the article was first named. Gauge are you still around to comment? -- Trovatore ( talk) 19:03, 21 August 2023 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||
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The same content is present at nowhere dense but I felt this deserves a separate page. I'll be creating a page on Volterra's function in the near future if someone doesn't beat me to it  :-) - Gauge 06:07, 23 Aug 2004 (UTC)
There is a slight inconsistency here. Either the intervals removed at each step are the "middle quarter of the remaining intervals" or they are centred on a/2^n. But they cannot be both. The first leads to measure of 0.5, the second to measure of 0.53557368... -- Henrygb 17:17, 25 Apr 2005 (UTC)
Let the set be called S. By construction, S contains no intervals (i.e. S contains points that are seperate from each other.). And the measure of a single point is 0. So how can the total measure be 1/2? On the other hand, the total length of removal is 1/2, hence remaining length must be 1/2. Hence, S must contains intervals of length greater than 0. Can somebody please help me resolve this? 108.162.157.141 ( talk) 01:53, 28 November 2013 (UTC)
This article needs to explain the hausdorff dimension of the Generalized Cantor set, as listed on the wikipage List of fractals by Hausdorff dimension, which is shown as
Could someone report on whether the particular name Smith–Volterra–Cantor set is attested in the references, or at least in the wild? The basic underlying idea here (not necessarily the specific sequence using ) is pretty standard and will inevitably come up in almost any real analysis course when clarifying the distinction between measure and category. The specific name used here, on the other hand, I do not recall seeing outside Wikipedia.
I'm concerned that this name could have been what an editor thought the construction should be called, which is something we're not supposed to do, though that may not have been as clear in 2004 when the article was first named. Gauge are you still around to comment? -- Trovatore ( talk) 19:03, 21 August 2023 (UTC)