The Computable Reals (alpha version)

On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
>
> >> Where is 0.101010101010101... on your list?
>
> >I'll be surely playing with that problem, is a next step,
>
> Wow. You insist that your list contains all computable
> numbers

No, YOU insist it is not but you won't give a definition for it.

Just the same ridicolousness.

> but when someone asks you to show it
> contains a certain _rational_ number all you can say
> is you'll surely be playing with that?

Yes, how strange, I have a life and bills too!

The rest I've snipped because it is just as incongruent and hypocrite.

Again, you can safely get lost.

-LV

In article
<455fd7be-5d9b-4ead-9c2a-4bbfa463baf2@y21g2000hsf.googlegroups.com>,
julio@diegidio.name wrote:

> On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> > >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> >
> > >> Where is 0.101010101010101... on your list?
> >
> > >I'll be surely playing with that problem, is a next step,
> >
> > Wow. You insist that your list contains all computable
> > numbers
>
> No, YOU insist it is not but you won't give a definition for it.

What?

You never _asked_ for that definition. Since you've been
talking about computable reals, I assumed you _knew_ the
definition.

In fact one version of the standard definition is that a
real number x is computable if there exists a Turing
machine T such that if you give T a positive integer
n as input then the output is an integer k such that
|x - k/n| <= 1/n.

> Just the same ridicolousness.

Erm, no. The ridoclousness would be the same if when
you asked for the definition (not that you ever did)
my reply was "I'm playing with that".

Your posts about computable numbers are suddenly about
a million times more ridiculous than they were: you're
been talking about "computable numbers" even though you
didn't know what a computable number _was_.

Wow.

> > but when someone asks you to show it
> > contains a certain _rational_ number all you can say
> > is you'll surely be playing with that?
>
> Yes, how strange, I have a life and bills too!
>
> The rest I've snipped because it is just as incongruent and hypocrite.
>
> Again, you can safely get lost.
>
> -LV

--
David C. Ullrich

In article
<455fd7be-5d9b-4ead-9c2a-4bbfa463baf2@y21g2000hsf.googlegroups.com>,
julio@diegidio.name wrote:

> On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> > >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> >
> > >> Where is 0.101010101010101... on your list?
> >
> > >I'll be surely playing with that problem, is a next step,
> >
> > Wow. You insist that your list contains all computable
> > numbers
>
> No, YOU insist it is not but you won't give a definition for it.

On the contrary, Cantor has already given a valid definition of a number
not in any given list, which is eminently constructable from that list.

On 13 Aug, 21:33, Virgil <Vir...@gmale.com> wrote:
> > No, YOU insist it is not but you won't give a definition for it.
>
> On the contrary, Cantor has already given a valid definition of a number
> not in any given list, which is eminently constructable from that list.

Oh, GREAT! I knew Cantor could disprove me.

So, please, go on and show this element eminently constructable from
the list I have given.

-LV

On 13 Aug, 21:26, "David C. Ullrich" <dullr...@sprynet.com> wrote:
> In article
> <455fd7be-5d9b-4ead-9c2a-4bbfa463b...@y21g2000hsf.googlegroups.com>,
>
> *ju...@diegidio.name wrote:
> > On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > > On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> > > >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
>
> > > >> Where is 0.101010101010101... on your list?
>
> > > >I'll be surely playing with that problem, is a next step,
>
> > > Wow. You insist that your list contains all computable
> > > numbers
>
> > No, YOU insist it is not but you won't give a definition for it.
>
> What?
>
> You never _asked_ for that definition. Since you've been
> talking about computable reals, I assumed you _knew_ the
> definition.

The definition of computables I know.

Where is the definition of completeness I am supposed to comply with?

> In fact one version of the standard definition is that a
> real number x is computable if there exists a Turing
> machine T such that if you give T a positive integer
> n as input then the output is an integer k such that
> *|x - k/n| <= 1/n.

So you give a definition of computable. Within *your* framework of
reference.

Super clever guy.

> > Just the same ridicolousness.

Indeed.

> Erm, no. The ridoclousness would be the same if when
> you asked for the definition (not that you ever did)
> my reply was "I'm playing with that".
>
> Your posts about computable numbers are suddenly about
> a million times more ridiculous than they were: you're
> been talking about "computable numbers" even though you
> didn't know what a computable number _was_.

Your logic, as I have already had the pleasure to point out, is just a
joke.

> Wow.

Indeed.

-LV

In article
<1ae80a02-620d-49d9-a68c-6c7808a704d8@l64g2000hse.googlegroups.com>,
julio@diegidio.name wrote:

> On 13 Aug, 21:26, "David C. Ullrich" <dullr...@sprynet.com> wrote:
> > In article
> > <455fd7be-5d9b-4ead-9c2a-4bbfa463b...@y21g2000hsf.googlegroups.com>,
> >
> > *ju...@diegidio.name wrote:
> > > On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > > > On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> > > > >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> >
> > > > >> Where is 0.101010101010101... on your list?
> >
> > > > >I'll be surely playing with that problem, is a next step,
> >
> > > > Wow. You insist that your list contains all computable
> > > > numbers
> >
> > > No, YOU insist it is not but you won't give a definition for it.
> >
> > What?
> >
> > You never _asked_ for that definition. Since you've been
> > talking about computable reals, I assumed you _knew_ the
> > definition.
>
> The definition of computables I know.
>
> Where is the definition of completeness I am supposed to comply with?

I'm not certain what you mean here by "completeness".
And I don't know why it matters. Whether or not this
has anything to do with what you mean when you say the
list is "complete", the question is whether the list
contains all the computable numbers. (It doesn't, by the way.)

I already said this a few posts up, by the way:

'We've all been _guessing_ that when you say the list is
"complete" you mean that it contains all the computable
numbers.

That's not what "complete" usually means, but it's the point
at issue here. _How_ do you prove that the list contains
all computable numbers?'

> > In fact one version of the standard definition is that a
> > real number x is computable if there exists a Turing
> > machine T such that if you give T a positive integer
> > n as input then the output is an integer k such that
> > *|x - k/n| <= 1/n.
>
> So you give a definition of computable. Within *your* framework of
> reference.

That's the definition. If the definition is different "in
your framework of reference" you need to _state_ your
own personal definition. Otherwise people will not know
what you're talking about.

See, if "computable number" means "positive integer" in
your private language then nobody's going to be that surprised
that you can construct a list of the computable numbers.

> Super clever guy.
>
> > > Just the same ridicolousness.
>
> Indeed.
>
> > Erm, no. The ridoclousness would be the same if when
> > you asked for the definition (not that you ever did)
> > my reply was "I'm playing with that".
> >
> > Your posts about computable numbers are suddenly about
> > a million times more ridiculous than they were: you're
> > been talking about "computable numbers" even though you
> > didn't know what a computable number _was_.
>
> Your logic, as I have already had the pleasure to point out, is just a
> joke.

It's very curious. Nobody here seems to be smart enough to
understand your work. Why don't you publish your proofs instead
of posting them here?

> > Wow.
>
> Indeed.
>
> -LV

--
David C. Ullrich

In article <48a243c4$0$1021$afc38c87@news.optusnet.com.au>,
"Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:

> <julio@diegidio.name> wrote in message
> news:9d3af44f-8119-469d-acd1-4bfed792a06e@25g2000hsx.googlegroups.com...
> On 12 Aug, 18:43, "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> > > As to why I believe (think) that the list is "complete": because it is
> > > the _complete_ (over N*) list of _all_ the possible infinite (over N*)
> > > binary expansions.
> >
> > No, that's not possible.
>
> In this context, funny statement to say the least.
>
> > > Indeed, what I have given IS _per definition_ the list of the
> > > "computable reals" (modulo the usual adjustments).
> >
> > No, you haven't. There _is_ a standard definition of "computable
> > real", and it simply doesn't appear anywhere in your post.
>
> Another funny statement, even more funny considering that the standard
> definition happens to correspond to mine were it not for your pre-
> judgement.
>
> I wander what you really don't know. For instance, it is far from a
> pleasure, apart from how improductive, to keep on these tones. You
> maybe don't take me for serious on this.
>
> -LV
>
> *****************************************
> I think the reason that some people use a dismissive tone is because of the
> tone you use.
>
> As I understand it, you purport to show a way of enumerating the computable
> reals. Your construction obviously doesn't work, as a simple diagonalisation
> argument will produce computable Reals not on the list.
>
> Do you accept that your construction contains an error? If you don't, then
> you are claiming that set theory is inconsistent, which is a pretty bold
> claim, particularly for a self-admitted beginner.

You haven't been paying attention. Bold claims are no problem -
he has a proof that the reals are countable, and the "boldness"
of this claim doesn't seem to make him suspect there may be an
error somewhere.

> If you accept that your construction is wrong, then you are basically asking
> for somebody to help you find the error in your construction. I can provide
> some assistance with that.
>
> Your construction can fail in two ways:
>
> 1. It doesn't construct a list at all, or
> 2. It constructs a list, but this does not include all the computable Reals.
>
> The first is the place to start.
>
> What is the first computable Real produced by your construction? What are
> the second and third computable Reals it produces?
>
> If you can't answer that, then your construction does not provide a list at
> all, and hence you don't even get to first base.
>
> So I would check that first.
>
> If you can demonstrate that it produces a list, then we can move onto the
> second possibility. I suspect we won't even get that far.
>
> HTH
>
>
> Peter Webb

--
David C. Ullrich

On 13 Aug, 11:25, David C. Ullrich <dullr...@sprynet.com> wrote:

> >Pardon me, how does pi-3 expands in binary?

> What does that matter? It's a computable number. So you're
> claiming it's on your list - you need to prove that.

No, it was Mr Bacarisse to claim pi-3 and other numbers are not.

I was with the quoted question trying to provoke him in getting into
the computables.

You are still off mark.

-LV

In article
<28fc7931-9f88-4933-9424-f5613f15d398@e53g2000hsa.googlegroups.com>,
julio@diegidio.name wrote:

> On 13 Aug, 21:33, Virgil <Vir...@gmale.com> wrote:
> > > No, YOU insist it is not but you won't give a definition for it.
> >
> > On the contrary, Cantor has already given a valid definition of a number
> > not in any given list, which is eminently constructable from that list.
>
> Oh, GREAT! I knew Cantor could disprove me.
>
> So, please, go on and show this element eminently constructable from
> the list I have given.

If "the list you have given" provides a method for finding the decimal
representation of the nth number in the list, then Cantor's construction
finds an unlisted number.

If "the list you have given" does not provide a method for finding the
decimal representation of the nth number in the list, in what format is
an nth number to be represented?

In article
<1ae80a02-620d-49d9-a68c-6c7808a704d8@l64g2000hse.googlegroups.com>,
julio@diegidio.name wrote:

> On 13 Aug, 21:26, "David C. Ullrich" <dullr...@sprynet.com> wrote:
> > In article
> > <455fd7be-5d9b-4ead-9c2a-4bbfa463b...@y21g2000hsf.googlegroups.com>,
> >
> > *ju...@diegidio.name wrote:
> > > On 13 Aug, 11:31, David C. Ullrich <dullr...@sprynet.com> wrote:
> > > > On Tue, 12 Aug 2008 22:14:35 -0700 (PDT), ju...@diegidio.name wrote:
> > > > >On 13 Aug, 00:36, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> >
> > > > >> Where is 0.101010101010101... on your list?
> >
> > > > >I'll be surely playing with that problem, is a next step,
> >
> > > > Wow. You insist that your list contains all computable
> > > > numbers
> >
> > > No, YOU insist it is not but you won't give a definition for it.
> >
> > What?
> >
> > You never _asked_ for that definition. Since you've been
> > talking about computable reals, I assumed you _knew_ the
> > definition.
>
> The definition of computables I know.

Is your definition compatible with that of "computable numbers" as
defined in http://en.wikipedia.org/wiki/Computable_number ?

If not, how does it differ?
>
> Where is the definition of completeness I am supposed to comply with?
>
> > In fact one version of the standard definition is that a
> > real number x is computable if there exists a Turing
> > machine T such that if you give T a positive integer
> > n as input then the output is an integer k such that
> > *|x - k/n| <= 1/n.
>
> So you give a definition of computable. Within *your* framework of
> reference.
>
> Super clever guy.
>
> > > Just the same ridicolousness.
>
> Indeed.
>
> > Erm, no. The ridoclousness would be the same if when
> > you asked for the definition (not that you ever did)
> > my reply was "I'm playing with that".
> >
> > Your posts about computable numbers are suddenly about
> > a million times more ridiculous than they were: you're
> > been talking about "computable numbers" even though you
> > didn't know what a computable number _was_.
>
> Your logic, as I have already had the pleasure to point out, is just a
> joke.
>
> > Wow.
>
> Indeed.
>
> -LV