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From: |-|ercules on 12 Jun 2010 12:44
"Colin" <colinpoakes(a)hotmail.com> wrote
>. Thus Cantor's diagonal argument cannot be used to produce
> uncountably many computable reals; at best, the reals formed from this
> method will be uncomputable."

OK, but you can make a superset including the computable reals
with the godel index.

It's not conceptually difficult to question Cantor's argument on a
hypothetical list. But there's little point going into detail, perhaps
if it was acknowledged modifying the diagonal results in a new
digit sequence that is not computable, then we could increase the
scope to work out the mechanics. But it wouldn't demonstrate
anything at this point, rather the opposite!

Herc

From: |-|ercules on 12 Jun 2010 12:46
correction.


"|-|ercules" <radgray123(a)yahoo.com> wrote

> perhaps
> if it was acknowledged modifying the diagonal (DID NOT) results in a new
> digit sequence that is not computable, then we could increase the
> scope


Herc
From: Mike Terry on 12 Jun 2010 13:37
"|-|ercules" <radgray123(a)yahoo.com> wrote in message
news:87h5s6FgveU1(a)mid.individual.net...
>
> Every possible digit sequence is computable to ALL (an INFINITE AMOUNT of)
finite initial substrings.
>
____________________________________________________________________________
_______________________
>
>
> 2 or 3 posters on sci.math have agreed with that statement.
>
> BTW: ALL (an INFINITE AMOUNT of) natural numbers are in "all natural
numbers"
> incase any of you want to feign comprehension disability.
>
> Is it too much for you to fathom that I disagree whether no box containing
the box numbers
> that don't contain their own box numbers is self referential on some
level? MAYBE, just MAYBE
> there is another explanation than sets larger than infinity?
>
> Do you believe there are numerous different digits (at finite positions)
all along the expansion
> of some reals that are not on the computable reals list?

I'm afraid that what you've just asked is strictly nonsense, because a
specific digit of an expansion of a real (like "7", or "2") can't be on a
computable reals list, because the list is a list of reals, not digits,
(duh! :-)

But I think I know what you meant to say...

Are you in fact trying to ask whether we believe there are specific reals
that have one or more of their finite prefixes that can't be computed? More
precisely, you're asking us do we believe there exists a real with
digit-sequence D, such that for some n the (finite) sequence
D(1),D(2)...D(n) is not computable?

Mike.

>
> What does that mean?
>
> The only interpretation is "There is a finite substring between 2 digits
(inclusive) that is not computable"
> which is a clear contradiction.




From: spudnik on 12 Jun 2010 15:14
Russels's paradoxi are all equivalent,
"I am the only Solopsist, existentially;
therefore, there is only (one) Universe at the momentbeing."

thus&so:
see the retrospective metastudy on glaciers by S. Fred Singer (and,
it is certainly fun to ask, Did he work for an oil company?, and
not obther with his awesome vitae .-)

thus&so:
what you have been posting is merely absurd at the syllogistic level,
hence, entirely "silly," where all known properties of
electromagnetism,
which are wavey, dysappear into a loose hydrodynamic metaphor,
replacing "energy" with "aether" -- a quaint mental spazzm. funny, as
all of this could be exposed, merely by taking some aspect
of a real two-hole experiment, like the actual details
of the uncited fullerene set-up, into account.

waves can ne'er be particles, whether a mathematical duality can
be applied in a formularium of a phenomenon a la momentum; for
instance,
How is a water-wave to be known as a particle ... um, a hydron?

look at his sad nonsequiters; yours are only misnomers & oxymora
("global" warming, when insolation is totally differential
from pole to equator e.g.). and, so, What'd you "understood of the
following?"

> A=Mc^2, where A is aether and M is matter,
> the following is easily understood: "If a body gives off the energy L
> in the form of radiation, its mass diminishes by L/c2."

--Stop BP's and Waxman's arbitrageurs' wetdream "Captain Tax as
according to the God-am WSUrinal" -- and they LOVE his '91 bill!
http://wlym.com
From: |-|ercules on 12 Jun 2010 19:23
"Mike Terry" <news.dead.person.stones(a)darjeeling.plus.com> wrote

[THE PROPOSITION]
>> Do you believe there are numerous different digits (at finite positions)
>> all along the expansion
>> of some reals that are not on the computable reals list?
>
> I'm afraid that what you've just asked is strictly nonsense, because a
> specific digit of an expansion of a real (like "7", or "2") can't be on a
> computable reals list, because the list is a list of reals, not digits,
> (duh! :-)
>
> But I think I know what you meant to say...
>
> Are you in fact trying to ask whether we believe there are specific reals
> that have one or more of their finite prefixes that can't be computed? More
> precisely, you're asking us do we believe there exists a real with
> digit-sequence D, such that for some n the (finite) sequence
> D(1),D(2)...D(n) is not computable?
>
> Mike.


No. I merely rephrased George Greene's claim. This will be the basis
for a FORMAL disproof that modifying the diagonal resulting in new numbers.


"George Greene" <greeneg(a)email.unc.edu> wrote
> On Jun 8, 4:29 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote:
>> YOU CAN'T FIND A NEW DIGIT SEQUENCE AT ANY POSITION ON THE COMPUTABLE REALS.
>
> OF COURSE you can't find it "at any position".
> It is INFINITELY long and the differences occur at INFINITELY MANY
> DIFFERENT positions!


OK SHOW OF HANDS!

Who agrees with George?


Herc

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