```Date: Feb 3, 2013 11:29 PM
Author: fom
Subject: Re: Matheology § 203

On 2/3/2013 9:20 PM, Virgil wrote:> In article> <bc3c4c0e-d017-49b3-a4f3-22aba84aa3c7@5g2000yqz.googlegroups.com>,>   WM <mueckenh@rz.fh-augsburg.de> wrote:>>> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:>>>>> We can say  "every line has the property that it>>>>> does not contain every initial segment of s">>>>> There is no need to use the concept "all".>>>>>>> Yes, and this is the only sensible way to treat infinity.>>>>>> So now we have a way of saying>>>>>> s is not a line of L>>>>>> e.g.  0.111...  is not a line of>>>>>> 0.1000...>>> 0.11000...>>> 0.111000....>>> ...>>>>>> because every line, l(n),  has the property that>>> l(n) does not  contain every  initial>>> segment of 0.111...>>>> But that does not exclude s from being in the list. What finite>> initial segment (FIS) of 0.111... is missing? Up to every line there>> is some FIS missing, but every FIS is with certainty in some trailing>> line. And with FIS(n) all smaller FISs are present.> But with no FIS are all present.>>>>> Is there a sensible way of saying>>> s is a line of L ?>>>> There is no sensible way of saying that 0.111... is more than every>> FIS.>> How about "For all f, (f is a FIS) -> (length(0.111...) > length(f))" .In view of WM's positions, length(0.111...) would haveto be the value given to a non-existent.  In Fregeandescription theory, this would be the null class.So, for all f, null>length(f).Next, WM would say that this is fine until thedomain of arguments to the relation '>' is restrictedto numbers.
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