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

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From: George Greene on 24 Jun 2010 11:13

On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote:

> It's the digit width of a SET of numbers.

IT *IS*NOT*.
In the first place, THIS IS A *LIST*, NOT a mere SET,
of numbers! In the second place, you are still refusing
to do this with THE RIGHT list, which is the list OF ALL FINITE
sequences. Doing it with all computable will UNDERcut your claim
because EVERY sequence in THAT list has wdith w (so you might
get away with abusing language long enough to claim that "the list"
had
width w). But in THE ACTUALLY RELEVANT CASE, individual (finite)
sequences-on-the-list have DIFFERENT widths and THERE IS NO MAXIMUM
width!

From: Graham Cooper on 24 Jun 2010 16:01

On Jun 25, 1:13 am, George Greene <gree...(a)email.unc.edu> wrote:
> On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
>
> > It's the digit width of a SET of numbers.
>
> IT *IS*NOT*.

IT IS TOO!

It's my definition it's my theorem.

All you have to do is put in your own words the corrollery
of this short proof.

Assumption. There exists a real number with a finite sequence
of digits that is not computable. Contradiction.

Therefore...... <take it away George!>

Herc

From: Graham Cooper on 24 Jun 2010 16:07

From: Graham Cooper on 24 Jun 2010 16:10

On Jun 24, 11:35 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 24/06/2010 5:09 PM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 24, 5:00 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >> On 24/06/2010 1:12 PM, Tim Little wrote:
>
> >>> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>> On 23/06/2010 5:00 PM, Tim Little wrote:
> >>>>> 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.
>
> >>> It is the very core of his argument: if pi were "contained in" the
> >>> infinite list
>
> >>> 3
> >>> 3.1
> >>> 3.14
> >>> 3.141
> >>> ...
>
> >>> then it would also be "contained in" any other list sharing the "all
> >>> prefixes" property, such as
>
> >>> 3.0000000
> >>> 3.1000000
> >>> 3.1428571. . .
> >>> 3.1414141
> >>> ...
>
> >>> It would even be "contained in" any list having that as a sublist, e.g.
>
> >>> 0.0000000
> >>> 3.0000000
> >>> 3.1000000
> >>> 1.0000000
> >>> 3.1428571. . .
> >>> 2.0934953
> >>> 0.5829345
> >>> 3.1414141
> >>> ...
>
> >>> The list of all computable reals is exactly such a list. Most
> >>> importantly, no property specific to pi is used here. Every real
> >>> would be "contained in" that list if we were to use Herc's broken idea
> >>> of "contained in".
>
> >> Ok, but his next step - all finite prefixes implies all infinite
> >> sequences - is false. So all it means is that his 'proof' contains two
> >> invalid steps rather than just one.
>
> >> Sylvia.
>
> > I've told you atleast 3 times specifically that is NOT an implication
> > of hc3. I put it in a implication formula -> are you amnesiac?
>
> I never said it was an implication *of* hc3. I say it's an implication
> *in* hc3.
>
>
>
> > As long as all permutations oo wide are in the set, (segmented,
> > appended to hitlers number, inverted, imputed, with any other
> > numbers you can think of) I don't care!
>
> You need to prove that they're all in the set, or you have nothing.
>
> > But one of these days
> > one of is going to confirm oo digits of every sequence are ALL THERE
>
> Sylvia.
>
>
>
>
That is no excuse you are still wrong. Something that is implied
is implied. You corrected the correction in place of admitting
you have been told

all finite prefixes -> all oo long sequences

is N O T hc3

you've been told 5 times now plus I explained it several
more times in this thread and you still carry on.

Learn to read!

Herc

From: Graham Cooper on 24 Jun 2010 16:14

On Jun 25, 6:01 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
> On Jun 25, 1:13 am, George Greene <gree...(a)email.unc.edu> wrote:
>
> > On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
>
> > > It's the digit width of a SET of numbers.
>
> > IT *IS*NOT*.
>
> IT IS TOO!
>
> It's my definition it's my theorem.
>
> All you have to do is put in your own words the corrollery
> of this short proof.
>
> Assumption. There exists a real number with a finite sequence
> of digits that is not computable. Contradiction.
>
> Therefore...... <take it away George!>
>
> Herc

Here we go. George will come up with the most muddled
quantified filled meaningless interpretaion with copious
references to FINITE sequences. And still deny it clearly
proves hc3

Herc