Can N be constructed?
in [Logic]
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From: Marshall on 10 Jun 2010 10:33 On Jun 10, 6:23 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > But I don't see why you should care whether William wants to engage in > this futile discussion or not. He's not preventing other conversations > from happening. That makes perfect sense, and is entirely defensible. But as near as I can tell, it isn't strictly true. Marshall
From: WM on 10 Jun 2010 10:40 On 10 Jun., 16:13, William Hughes <wpihug...(a)hotmail.com> wrote: > After any finite number of steps the set of remaining lines > cannot be empty. No. After any possible step the set of remaining lines cannot be empty. > > Look! Over There! A Pink Elephant! > > After an infinite number of steps the set of remaining lines > cannot be empty. How would you get to an infinite number of steps when each step has another finite number? Regards, WM
From: WM on 10 Jun 2010 10:46 On 10 Jun., 16:10, William Hughes <wpihug...(a)hotmail.com> wrote: > > No, I don't think so. After an infinite number of steps, where > > at each step a (finite) line is removed from the list, you end > > up with no lines at all. > > Well this depends on defining what you "end up with" > > If your definition is (the very reasonable) "you end up > with any lines that have been written down but not erased", > then you end up with no lines as every line you write down > gets erased. That is wrong. Only every line *before the last one constructed* is erased. Only if "all lines" can be constructed, then all lines are erased and are not erased. This sheds some doubt on the assertion that all lines can be constructed. > > However, I think in this context saying that "you end up > with the limit line 111..." is better. However, this > definition has its problems. The main one is that you > "end up with" a line that you never write down. How could that line be created? Where does ot come from? Is it created by construction of infinitely many lines? One 1 from each? Up to any possible step this supposition is false. > > Note, however, that in neither case do you end up with > a line from the list. It is impossible to end up with a line that is not in the list, because only such lines are ever constructed. Regards, WM
From: Daryl McCullough on 10 Jun 2010 12:43 herbzet says... >As I wrote in another post to sci.logic recently >news:4C05D711.A917D173(a)gmail.com it is my opinion that the indulgence >of these trolls has a severely degenerative effect on the newsgroup. >I see this not only in sci.logic, but in a number of other newsgroups >to which I subscribe. Actually, it seems to me that for several groups, there would be no substantial posts at all if it weren't for posts correcting the mistakes of crackpots. -- Daryl McCullough Ithaca, NY
From: herbzet on 10 Jun 2010 13:19
Daryl McCullough wrote: > herbzet says... > > > As I wrote in another post to sci.logic recently > > news:4C05D711.A917D173(a)gmail.com it is my opinion that the indulgence > > of these trolls has a severely degenerative effect on the newsgroup. > > I see this not only in sci.logic, but in a number of other newsgroups > > to which I subscribe. > > Actually, it seems to me that for several groups, there would be > no substantial posts at all if it weren't for posts correcting > the mistakes of crackpots. I don't think your observation and mine are contradictory in the least. -- hz |