How Wide Do All The Possible Computed Digit Sequences Go? [Math]

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From: Tim Little on 23 Jun 2010 03:00

On 2010-06-23, Sylvia Else <sylvia(a)not.here.invalid> wrote:
> On the face of it, line n contains the n digits of pie,
> sequentially, and in order. I suppose it can be conceded that the
> infinite list contains Pi.

It can't be conceded, as it is simply false. The predicate "list L
contains x" means exactly that there exists n in N such that L_n = x.
The list does not contain pi since there is no such n. It really is
that simple.

It does satisfy a much looser property: there exists a sublist S such
that lim S = pi. In general you can form a set of real numbers
closure(L) = { x in R | exists sublist S of L such that lim S = x }
which you could call the "closure" of a list L.

Then you could say that pi is in the closure of the list, but pi is
certainly not in the list itself.

Herc does not know the difference.

- Tim

From: Graham Cooper on 23 Jun 2010 03:03

On Jun 23, 5:00 pm, Tim Little <t...(a)little-possums.net> wrote:
> On 2010-06-23, Sylvia Else <syl...(a)not.here.invalid> wrote:
>
> > On the face of it, line n contains the n digits of pie,
> > sequentially, and in order. I suppose it can be conceded that the
> > infinite list contains Pi.
>
> It can't be conceded, as it is simply false. The predicate "list L
> contains x" means exactly that there exists n in N such that L_n = x.
> The list does not contain pi since there is no such n. It really is
> that simple.
>
> It does satisfy a much looser property: there exists a sublist S such
> that lim S = pi. In general you can form a set of real numbers
> closure(L) = { x in R | exists sublist S of L such that lim S = x }
> which you could call the "closure" of a list L.
>
> Then you could say that pi is in the closure of the list, but pi is
> certainly not in the list itself.
>
> Herc does not know the difference.
>
> - Tim

How many digits in order of pi are below this line
if interpreted mathematically?

____________

3
31
314
....

From: Sylvia Else on 23 Jun 2010 03:32

On 23/06/2010 5:00 PM, Tim Little wrote:
> On 2010-06-23, Sylvia Else<sylvia(a)not.here.invalid> wrote:
>> On the face of it, line n contains the n digits of pie,
>> sequentially, and in order. I suppose it can be conceded that the
>> infinite list contains Pi.
>
> It can't be conceded, as it is simply false. The predicate "list L
> contains x" means exactly that there exists n in N such that L_n = x.
> The list does not contain pi since there is no such n. It really is
> that simple.
>

Well, OK. Though I can't see how it makes any difference to Herc's
argument, since I could never see what role it played anyway.

Sylvia.

From: Sylvia Else on 23 Jun 2010 03:35

On 23/06/2010 5:03 PM, Graham Cooper wrote:
> On Jun 23, 5:00 pm, Tim Little<t...(a)little-possums.net> wrote:
>> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>
>>> On the face of it, line n contains the n digits of pie,
>>> sequentially, and in order. I suppose it can be conceded that the
>>> infinite list contains Pi.
>>
>> It can't be conceded, as it is simply false. The predicate "list L
>> contains x" means exactly that there exists n in N such that L_n = x.
>> The list does not contain pi since there is no such n. It really is
>> that simple.
>>
>> It does satisfy a much looser property: there exists a sublist S such
>> that lim S = pi. In general you can form a set of real numbers
>> closure(L) = { x in R | exists sublist S of L such that lim S = x }
>> which you could call the "closure" of a list L.
>>
>> Then you could say that pi is in the closure of the list, but pi is
>> certainly not in the list itself.
>>
>> Herc does not know the difference.
>>
>> - Tim
>
>
> How many digits in order of pi are below this line
> if interpreted mathematically?

What does that question mean? In particular, what does "digits in order
of pi" mean?

Perhaps you could give some example lists, with the answer in each case.

Sylvia.

>
> ____________
>
> 3
> 31
> 314
> ...

From: Graham Cooper on 23 Jun 2010 04:43

On Jun 23, 5:35 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 23/06/2010 5:03 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 23, 5:00 pm, Tim Little<t...(a)little-possums.net> wrote:
> >> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote:
>
> >>> On the face of it, line n contains the n digits of pie,
> >>> sequentially, and in order. I suppose it can be conceded that the
> >>> infinite list contains Pi.
>
> >> It can't be conceded, as it is simply false. The predicate "list L
> >> contains x" means exactly that there exists n in N such that L_n = x..
> >> The list does not contain pi since there is no such n. It really is
> >> that simple.
>
> >> It does satisfy a much looser property: there exists a sublist S such
> >> that lim S = pi. In general you can form a set of real numbers
> >> closure(L) = { x in R | exists sublist S of L such that lim S = x }
> >> which you could call the "closure" of a list L.
>
> >> Then you could say that pi is in the closure of the list, but pi is
> >> certainly not in the list itself.
>
> >> Herc does not know the difference.
>
> >> - Tim
>
> > How many digits in order of pi are below this line
> > if interpreted mathematically?
>
> What does that question mean? In particular, what does "digits in order
> of pi" mean?
>
> Perhaps you could give some example lists, with the answer in each case.
>
> Sylvia.
>
>
>
>
>
> > ____________
>
> > 3
> > 31
> > 314
> > ...

Huh? I'm not explaining trivial items to you.

Your "mutilation" of herc_can't_3 was proved erronous
and it stands. There are other terms than contains where it holds
so what is your argument? Your disproof was wrong and you
won't admit you were wrong. Now you are shifting your erronous
claim to a termi ology issue. Either give a proper disproof
or ceasevyour eternal complaints. Hc3 stands. The ball
is in your court to prove otherwise.

Herc