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Topic: Matheology § 222 Back to the roots
Replies: 9   Last Post: Apr 17, 2013 11:24 PM

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Alan Smaill

Posts: 748
Registered: 1/29/05
Re: Matheology § 222 Back to the roots
Posted: Mar 11, 2013 9:26 AM
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WM <mueckenh@rz.fh-augsburg.de> writes:

> On 11 Mrz., 12:51, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 9 Mrz., 16:00, William Hughes <wpihug...@gmail.com> wrote:
>> >> So this is WM's explanation.
>>
>> >> When he says
>>
>> >> No findable line of L is coFIS
>> >> with d

>>
>> >> and
>>
>> >> g is coFIS with d
>>
>> >> he is not using the same d.
>>
>> >> d like L_m is changable.
>>
>> >> So let us use (d) to indicate the function.
>> >> The function (d) is not changable, though
>> >> its value may be.

>>
>> > What do you understand by the not changeable function (d)?
>>
>> Can you understand that there is a function which, given any natural
>> number n, can return the first n digits of the decimal expansion of pi?

>
> Of course. There is even a much simpler case, namely the function that
> given n return n digits of 1/9. But we have to distinguish between
> this function, abbreviated by "0.111..." and its values
> 0.1
> 0.11
> 0.111
> ...
>
> Note here no actual infinity is involved unless 0.111... is assumed to
> be a decimal fraction with more than any finite number of 1's.


And can you understand that it is possible to give a potentially
infinite list of potentially infinite lists of digits, by a function f
of two naturals, such that for every n,m, f(n,m) is the mth
digit of the mth list?

Still no actual infinity, and the function is a fixed set of instructions.

>
> Regards, WM


--
Alan Smaill



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