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From: |-|ercules on 2 Jul 2010 11:25
As the length of the list of computable reals->oo, the length of all possible digit sequences on the list->oo.

What's your explanation for what happens if the list IS infinitely long? All sequences doesn't quite make it
to infinity?? It misses some?

Herc

--
"George Greene" <greeneg(a)email.unc.edu> wrote
>> Are you really that stupid to assume ...?
>
> I don't NEED to ASSUME!
From: David R Tribble on 2 Jul 2010 11:52
|-|ercules wrote:
> As the length of the list of computable reals->oo, the length of all possible digit sequences on
> the list->oo.
>
> What's your explanation for what happens if the list IS infinitely long? All sequences doesn't quite
> make it to infinity?? It misses some?

1. Can you tell us the difference, if any, between a list that
"approaches infinitely length" and a list that "has infinite length"?

2. The infinitely-wide list contains the digit sequence .333...,
so what is the next digit sequence that follows it in the list?
From: |-|ercules on 3 Jul 2010 20:21
"David R Tribble" <david(a)tribble.com> wrote ...
> |-|ercules wrote:
>> As the length of the list of computable reals->oo, the length of all possible digit sequences on
>> the list->oo.
>>
>> What's your explanation for what happens if the list IS infinitely long? All sequences doesn't quite
>> make it to infinity?? It misses some?
>
> 1. Can you tell us the difference, if any, between a list that
> "approaches infinitely length" and a list that "has infinite length"?
>
> 2. The infinitely-wide list contains the digit sequence .333...,
> so what is the next digit sequence that follows it in the list?

I'm not sure it's worth answering these questions without you acknowledging whether you
agree with my other answers in the thread "As the length...".

Keep aus.tv in the groups if you want to ensure I will read your response.

Herc
From: George Greene on 5 Jul 2010 01:32
On Jul 2, 11:25 am, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> As the length of the list of computable reals->oo,

This is completely ridiculous. The length of the list of computable
reals
NEVER APPROACHES ANYthing! The length of the list of computable
reals IS A CONSTANT! It is ALWAYS w (the smallest infinity), AS is
the WIDTH
of that list (every real on that list is w digits wide).

> the length of all possible digit sequences on the list->oo.

This is just incoherent. THERE IS NO SUCH THING as "a possible digit
sequence on the list",
let alone "all possible digit sequences on the list". A sequence IS
EITHER ON THE LIST OR IT ISN'T,
FACTUALLY, NOT "possibly"! This list does NOT grow over time, or
APPROACH anything!
It IS ALWAYS, in full, THE WHOLE list of all and only the computable
reals.
It is NOT POSSIBLE, EVER, for ANY NON-computable real to be on this
list!


> What's your explanation for what happens if the list IS infinitely long?

You CANNOT SAY "if" here! The list FACTUALLY IS infinitely long!
ALL the time! Our explanation "if" that is the case IS THE SAME
explanation that
we have always been giving! What happens is that MOST reals ARE NOT
ON the list
because most reals are not computable (and neither is this list, for
that matter).
From: George Greene on 6 Jul 2010 14:37
On Jul 2, 11:52 am, David R Tribble <da...(a)tribble.com> wrote:
> |-|ercules wrote:
> 1. Can you tell us the difference, if any, between a list that
> "approaches infinitely length" and a list that "has infinite length"?

No, he can't, but I can.
In the first place, he DIDN'T SAY "approaches infinitely length".
He said "as the length of the list ... --> oo".
He, as usually, did NOT MEAN what he said.
This has somewhat to do with the confusion between a variable and a
constant.
That would be a great test question, actually ("Herc, do you know the
difference between
a variable and a constant? This list of all computable reals -- is it
a variable or a constant?")
If you have a list VARIABLE into which you are INTENDING to STORE the
list of all computable reals,
then, yes, the length of the VARIABLE can approach infinity. But if
you are just thinking of the
infinite list itself (as a MATH thing, as a constant, NOT a variable
being updated in a procedural language),
then that is a constant and (obviously) has a constant length which
canNOT approach anything.
What Herc MEANS by "As the length of the list of computable reals->oo"
is,
"As the value of SOME INDEX VARIABLE h that *I* am using to step
through
the list of all computable reals increases -- WITHOUT limit, i.e,
withOUT approaching
anything in particular -- the width w or logarithm-of-the-size-of a
certain class-of-classes matchable
with prefixes of items occurring IN THIS INITIAL SEGMENT of the list,
also increases without limit."
The classes in question are parameterized by their width, and are, for
each width w, the
classes of all-digit-strings-of-length-w. In other words, as you go
down the list, it eventually becomes the
case that there have been 10 entries starting with each of 0 through
9, then later, you reach the point where
100 of the entries have started with all of 00 through 99, and then by
some later point, there will also have
been 1000 entries starting with all of 000 through 999, etc.

This is of course all true but it is irrelevant; you could (of course)
accomplish the EXACT same thing
JUST by LISTING ALL THE NUMBERS FROM 1 on up, with a few inversions
for leading zeros.
But of course Herc would never do it that way, because that way, it
would be obvious that it simply
had nothing whatsoever to do with infinity or with reals.

width w

>
> 2. The infinitely-wide list contains the digit sequence .333...,
> so what is the next digit sequence that follows it in the list?

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