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From: George Greene on 16 Jun 2010 11:24
On Jun 16, 5:39 am, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> The list of computable reals contains every digit (in order) of all possible infinite sequences.
>
> Derivation
>
> Given the increasing finite prefixes of pi
>
> 3
> 31
> 314
> ..
>
> This list contains every digit (in order) of the infinite expansion of pi..
>
> Given the increasing finite prefixes of e
>
> 2
> 27
> 271
> ..
>
> This list contains every digit (in order) of the infinite expansion of e.

That's true, but that's only two cases.
HOW DO YOU GET from two cases to "every" computable list of
this type, or from there TO ANY UNcomputable anything??
The short answer is that YOU DON'T.

> Given the increasing finite prefixes of ALL infinite expansions,

A PREFIX of an infinite expansion IS FINITE.

> that list contains every digit (in order) of every infinite expansion.

Well, sure, THAT list does, but that list is, like all the two lists
above,
a list OF FINITE strings! THAT list has NOTHING WHATSOEVER TO DO
with this list of "all computable reals"that you keep invoking!
Most computable reals are (like your two above) INFINITELY long, yet
your two infinitely long lists above have only FINITELY WIDE ELEMENTS
ON them!
You don't even NEED TO GO to infinitely wide computable reals to get
the
kind of "containment" that YOU are talking about!

> So herc_cant_3 is true.
> The list of computable reals contains every digit (in order) of all possible infinite sequences.

If this is what you mean by "contain" then it simply doesn't mean
anything.
The fact that there are infinitely long lists of FINITE strings
that contain every FINITE prefix of every real (computable or not)
does NOT imply that those are lists OF every real.
Those lists obviously do not contain ANY reals (computable or not)
unless you adopt some convention about abbreviating
..5000000000000000000000000000000000000..etc
as
..5

From: Tim Little on 16 Jun 2010 21:48
On 2010-06-16, |-|ercules <radgray123(a)yahoo.com> wrote:
> defn(herc_cant_3)
> The list of computable reals contains every digit (in order) of all
> possible infinite sequences.

So what? So does the finite list:

000...
111...
222...
333...
444...
555...
666...
777...
888...
999...

For any digit in any position of any possible infinite sequence of
decimal digits, there is an entry in the list that has that digit in
the correct position. What do you think that proves?


- Tim
From: |-|ercules on 16 Jun 2010 22:27
"Tim Little" <tim(a)little-possums.net> wrote
> On 2010-06-16, |-|ercules <radgray123(a)yahoo.com> wrote:
>> defn(herc_cant_3)
>> The list of computable reals contains every digit (in order) of all
>> possible infinite sequences.
>
> So what? So does the finite list:
>
> 000...
> 111...
> 222...
> 333...
> 444...
> 555...
> 666...
> 777...
> 888...
> 999...
>
> For any digit in any position of any possible infinite sequence of
> decimal digits, there is an entry in the list that has that digit in
> the correct position. What do you think that proves?
>
>
> - Tim

This list has 3 digits (in order) of pi.

3
31
314

Yours does not.

Herc

From: Tim Little on 17 Jun 2010 00:33
On 2010-06-17, |-|ercules <radgray123(a)yahoo.com> wrote:
> "Tim Little" <tim(a)little-possums.net> wrote
>> 000...
>> 111...
>> 222...
>> 333...
>> 444...
>> 555...
>> 666...
>> 777...
>> 888...
>> 999...
>
> This list has 3 digits (in order) of pi.
>
> 3
> 31
> 314
>
> Yours does not.

Sure it does. The first digit of the fourth row (a 3) is in the
correct position, the second digit in the second row (a 1) is in its
correct position, and the third digit in the fifth row (a 4) is in the
correct position.

The 3 is to the left of the 1 and 4, the 1 is between the 3 and 4, and
the 4 is to the right of both. So is has the first three digits of
pi, in the correct order.


- Tim
From: George Greene on 17 Jun 2010 00:53
On Jun 16, 10:27 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
> This list has 3 digits (in order) of pi.
>
> 3
> 31
> 314
>
> Yours does not.

Well, you DID NOT SAY "contains (in order)"
in your original formulations -- you JUST said "contains".
But it still doesn't matter.
You can still do this in a ONE-element list.
You can also still do it with a list consisting of ONLY FINITE
strings.
So the mere fact that a list has what you claim to want it to have
here
SIMPLY DOES NOT *MEAN* anything, fool.

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