Can N be constructed?
in [Logic]
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From: herbzet on 12 Jun 2010 19:58 George Greene wrote: > WM wrote: > > >The list is incomplete after every step. > > Virgil wrote: > > But not after all steps, which makes motion possible. > > WM is just willfully exploiting little holes in ENGLISH at this point. > "All" is AMBIGUOUS in common usage, so much so that it just > ought to be outlawed in advance in this discussion. > "Every" is correct; it is singular; it is about each (AND every) > INDIVIDUAL. > "All" is also sometimes used that way but we clearly have to have A > DIFFERENT > word to mean "the entire collection of" some things, considered as ONE > thing. > EVERY natural number is finite and is odd or even, but ALL natural > numbers form > an infinite collection. > > WM continually tries to pretend that he does not understand this > distinction. > Originally, I didn't know he was pretending; I thought he was just > stupid. > He actually continues to be stupid in belaboring these points, but in > a more perverse way. It's called "willful stupidity". <yawn> -- hz Against stupidity, the gods themselves contend in vain. - Schiller -
From: WM on 13 Jun 2010 06:21 On 12 Jun., 22:05, Virgil <Vir...(a)home.esc> wrote: > > Correct. But 1/9 can be constructed, i.e., every digit can be > > determined by an algorithm. Same holds for sqrt(2) and pi. But the big > > error was to assume that an infinite sequence could also exist without > > an algorithm and define a number. The number would only be defined > > when the last digit of the sequence was known. > > How does one ever "know" the "last digit" of a sequence which does not > have a last digit, for example, 0.333...? Never. > > Nevertheless, there is a well-defined number in decimal arithmetic > defined by that sequence. No, not by that sequence. The number is defined by a word, in there are many words, each defining it: 1/3 0.333... one over three ein Drittel 2:6 There is no infinite sequence defining it. Only from the finite definition, you can obtain every digit of the sequence. Regards, WM
From: Jesse F. Hughes on 13 Jun 2010 09:28 David R Tribble <david(a)tribble.com> writes: > Virgil wrote: >>> [Mathematical encryption encoding] >>> So there are important, even essential, areas of mathematics in which >>> physics has absolutely no part. >> > > WM wrote: >> Who does that coding? Brains, pencils, computers? What would happen >> without matter, without energy, without physics? > > I believe this kind of logical error is a "domain error", or simply a > "reification fallacy": > http://en.wikipedia.org/wiki/Reification_(fallacy) > > Abstract ideas are encoded in our physical brains, yes. > But how does that turn mathematical and logic equations > into physics equations? Simpler: if WM's argument made any sense at all, it would follow that poetry is also a branch of physics. -- "And that's what we do. We put in more troops to get to a position where we can be in some other place. The question is, who ought to make that decision? The Congress or the commanders? And as you know, my position is clear. I'm the commander guy." --- George W. Bush
From: Virgil on 13 Jun 2010 14:05 In article <93a79992-2f0a-4e51-8256-203a1396f4ea(a)i28g2000yqa.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 12 Jun., 22:05, Virgil <Vir...(a)home.esc> wrote: > > > > Correct. But 1/9 can be constructed, i.e., every digit can be > > > determined by an algorithm. Same holds for sqrt(2) and pi. But the big > > > error was to assume that an infinite sequence could also exist without > > > an algorithm and define a number. The number would only be defined > > > when the last digit of the sequence was known. > > > > How does one ever "know" the "last digit" of a sequence which does not > > have a last digit, for example, 0.333...? > > Never. > > > > Nevertheless, there is a well-defined number in decimal arithmetic > > defined by that sequence. > > No, not by that sequence. The number is defined by a word, in there > are many words, each defining it: > 1/3 > 0.333... > one over three > ein Drittel > 2:6 > > There is no infinite sequence defining it. There is in my world. It is a shame hat WM's world is so much smaller. > Only from the finite > definition, you can obtain every digit of the sequence. And from any such sequence, one can find a number.
From: WM on 13 Jun 2010 15:08
On 13 Jun., 20:05, Virgil <Vir...(a)home.esc> wrote: > In article > <93a79992-2f0a-4e51-8256-203a1396f...(a)i28g2000yqa.googlegroups.com>, > > > > > > WM <mueck...(a)rz.fh-augsburg.de> wrote: > > On 12 Jun., 22:05, Virgil <Vir...(a)home.esc> wrote: > > > > > Correct. But 1/9 can be constructed, i.e., every digit can be > > > > determined by an algorithm. Same holds for sqrt(2) and pi. But the big > > > > error was to assume that an infinite sequence could also exist without > > > > an algorithm and define a number. The number would only be defined > > > > when the last digit of the sequence was known. > > > > How does one ever "know" the "last digit" of a sequence which does not > > > have a last digit, for example, 0.333...? > > > Never. > > > > Nevertheless, there is a well-defined number in decimal arithmetic > > > defined by that sequence. > > > No, not by that sequence. The number is defined by a word, in there > > are many words, each defining it: > > 1/3 > > 0.333... > > one over three > > ein Drittel > > 2:6 > > > There is no infinite sequence defining it. > > There is in my world. It is a shame hat WM's world is so much smaller. Every term of a sequence "counts". Every term of a sequence must be known, if the number defined by that sequence is to be known. (An unknown definition is not a definition!). But it is impossible to know every term of an infinite sequence (unless one knows it by another means, like a finite definition), because the sequence is never finished. What you think or believe or even have learned in school is wrong. A definition D defines a sequence S: D ==> S. In your world people think that would imply S ==> D. That is an error. > > > Only from the finite > > definition, you can obtain every digit of the sequence. > > And from any such sequence, one can find a number Yes. But then you don't need the sequence. Who uses an infinite array of 3's instead of 1/3? You would not be able to obtain a number from the sequence 0.111111111111111111111111111111111111111111111111111111111111 here I stopp, but even from 10^100^10000 digits you could not say what number is meant in the end. Sorry, probably you will not be willing to grasp that, and will continue to believe in uncountability and implication reversal. Nevertheles, this is one of the most spectacular mistakes ever committed in history of mankind. Regards, WM |