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Re: Matheology � 203
Posted:
Feb 3, 2013 11:50 PM
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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))" .
>
> It makes perfect sense to those not permanently encapsulated in
> WMytheology.
By the way, Mückenheim's crap is as idiotic from an intuitionistic point of
view as it is classically. Intuitionists do not have any problems
distinguishing the numbers 0,1...1 with finitely many digits and the
sequence formed by these numbers resp. the infinite decimal fraction
0,11....
--
Neueste Forschungsergebnisse aus deutschen Spitzenhochschulen. Heute von
Prof. Dr. Wolfgang Mückenheim, Mathematikkoryphäe der FH Augsburg, aus
seiner Postille "Physical constraints of numbers": "Even some single
numbers smaller than 2^10^100 ... do not exist."
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