Galileo's Paradox
in [Math]
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From: Virgil on 7 Dec 2006 14:05 In article <457822A4.1000103(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/7/2006 1:30 AM, David Marcus wrote: > > Eckard Blumschein wrote: > >> On 12/6/2006 5:35 AM, David Marcus wrote: > >> > Eckard Blumschein wrote: > >> > >> >> You did not understand that I am using Fourier transform as an example. > >> > > >> > Example of what? > >> > >> a typical mistake when using the immediate value. > > > > Be specific: what is the mistake? > > Ask Hendrik van Hees who could not explain a result differing from a > printed one just by the factor 2. He uttered this in sci.physics.research Examples of physcists phucking up are not relevant to mathematics. > Set theory considers real numbers to be existing numbers, not just > fictions. From this point of view, one cannot admit that a number may be > void even if it turns out to be useless and maybe even misleading. Examples of physcists phucking up are not relevant to mathematics.
From: Michael Press on 7 Dec 2006 20:50 In article <1165466931.523088.27190(a)j44g2000cwa.googlegroups.com>, imaginatorium(a)despammed.com wrote: > fallaciousness [is there a word 'fallacity'?] fallaciousness yes; fallacity no, and too close to felicity. `Falsity' is good English; also falsehood. When out on a limb try climbing back to the trunk. -- Michael Press
From: Mike Kelly on 8 Dec 2006 09:37 Six wrote: > On 6 Dec 2006 07:08:46 -0800, "Mike Kelly" <mk4284(a)bris.ac.uk> wrote: <snip> > >The set of finite binary strings is a subset of the set of finite > >decimal strings. > > I confess I hadn't fully appreciated this simple point, that > together with the fact that the strings just are, so to speak, the natural > numbers (in a given base). I'd say the strings are a representation of the set of natural numbers. I'd certainly expect the sets of strings and the set of natural numbers to be the same size. > >Then b) precludes them being the same size. > > > >They are also both the same size as the set of natural numbers. > > > >Thus they are the same size as each other. > > > >Contradiction. > > One is driven to the conclusion that there is no base-independent > size for the natural numbers. One is driven to the conclusion that EITHER a proper subset can be the same size as its superset OR that there is no base-independent size for the natural numbers. Frankly the latter makes no sense whatsoever to me for any reasonable interpretation of "the natural numbers". > This does not make the discussion of the relative size of, for > example, natural numbers and squares meaningless. It's just that a given > base would have to be understood, and that whatever is said about the > relative size of the two sets is understood to apply mutatis mutandis to > any other base. So you really believe "the set of natural numbers represented in base 10" is a different set from "the set of natural numbers represented in base 2"? Hmm. >But for me at least, it has certainly opened my eyes to the > implications of the original argument. > > Much appreciated, > > Six Letters Well... you're welcome, I guess. -- mike.
From: Eckard Blumschein on 8 Dec 2006 10:47 On 12/7/2006 8:05 PM, Virgil wrote: > In article <457822A4.1000103(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/7/2006 1:30 AM, David Marcus wrote: >> > Eckard Blumschein wrote: >> >> On 12/6/2006 5:35 AM, David Marcus wrote: >> >> > Eckard Blumschein wrote: >> >> >> >> >> You did not understand that I am using Fourier transform as an example. >> >> > >> >> > Example of what? >> >> >> >> a typical mistake when using the immediate value. >> > >> > Be specific: what is the mistake? >> >> Ask Hendrik van Hees who could not explain a result differing from a >> printed one just by the factor 2. He uttered this in sci.physics.research > > Examples of physcists phucking up are not relevant to mathematics. > > >> Set theory considers real numbers to be existing numbers, not just >> fictions. From this point of view, one cannot admit that a number may be >> void even if it turns out to be useless and maybe even misleading. > > Examples of physcists phucking up are not relevant to mathematics. You meant physicists. HvH is a reputable one. But what phucking stands for?
From: Eckard Blumschein on 8 Dec 2006 10:49
On 12/7/2006 8:05 PM, Virgil wrote: > In article <457822A4.1000103(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/7/2006 1:30 AM, David Marcus wrote: >> > Eckard Blumschein wrote: >> >> On 12/6/2006 5:35 AM, David Marcus wrote: >> >> > Eckard Blumschein wrote: >> >> >> >> >> You did not understand that I am using Fourier transform as an example. >> >> > >> >> > Example of what? >> >> >> >> a typical mistake when using the immediate value. >> > >> > Be specific: what is the mistake? >> >> Ask Hendrik van Hees who could not explain a result differing from a >> printed one just by the factor 2. He uttered this in sci.physics.research > > Examples of physcists phucking up are not relevant to mathematics. > > >> Set theory considers real numbers to be existing numbers, not just >> fictions. From this point of view, one cannot admit that a number may be >> void even if it turns out to be useless and maybe even misleading. > > Examples of physcists phucking up are not relevant to mathematics. You meant physicists. HvH is a reputed one. But what 'phucking up' stands for? |