fom
Posts:
1,098
Registered:
12/4/12
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Re: Matheology § 203
Posted:
Feb 3, 2013 5:04 PM
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On 2/3/2013 3:58 PM, WM 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.
>
>> 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. And every FIS is in a line.
Do you mean "is in some line"?
As in "there exists a line containing a given FIS"
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