Re: Cantor's diagonal proof wrong?

From: HERC777 (herc777_at_hotmail.com)
Date: 11/19/04 

Date: 19 Nov 2004 14:00:27 -0800

"Jesse F. Hughes" <jesse@phiwumbda.org> wrote
> herc777@hotmail.com (HERC777) writes:
>
> > "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message ..
> >> herc777@hotmail.com (HERC777) writes:
> >>
> >> More lame proof-by-Herc's-infallible-assertion. You've replaced the
> >> first proof-by-assertion with a weaker but still lame
> >> proof-by-assertion.
> >>
> >> If it's famous, then you should be mighty embarrassed.
> >
> >
> > I'm the one putting mathematics to paper here, find a fault in my proof,
> > actually back up YOUR negative presumptuous assertions HYPOCRITE!
> >
> >> > proof a random sequence contains pi :
> >> >
>
> >> > probability of segment of length n contains first n digits of pi =
> >> > 0.1^n.
>
> >> > given any n, the probalility > 0
>
> >> > limit as number of segments -> oo of probability of atleast one
> >> > segment equaling pi = 1
> >
> > Which clearly delineated step are you whining about?
>
> None of this makes any particular sense to me, aside from the possible
> exception of the first statement. But just to be precise, where did
> that "limit as number..." claim come from? It doesn't follow anything
> above at all.

> >> > probability of segment of length n contains first n digits of pi =
> >> > 0.1^n.
>
> >> > given any n, the probalility > 0

1/ forall n, P(random digit sequence of length n = 1st n digits of pi)
    = 0.1^n

 ->

2/ forall n, P(random digit sequence of length n = 1st n digits of pi)
> 0

Do you follow step 2 now? Countable infinity logic must be painful to
comprehend for people here, takes a bit of prodding.

>
> >> >> It is possible that the outcome of your experiment is this:
> >> >>
> >
> > You missed the implied RANDOM toss, this implies any
> > specific structured result is incorrect.
>
> My outcome is a logical possibility given random tosses. It isn't
> "Chaitin-random", but Chaitin-random has nothing to do with what is a
> possible outcome of a sequence of random events. Indeed, the outcome
> I gave
>
> > >> Person Coin sequence
> > >> 1 HTTTTTTTTTTTTTT...
> > >> 2 HHTTTTTTTTTTTTT...
> > >> 3 HHHTTTTTTTTTTTT...
> > >> 4 HHHHTTTTTTTTTTT...
> > >> ...
> > >> n HH..HTTTTTTTTTT...
> > >> \___/
> > >> n heads, followed only by tails.
>
> is not more or less likely than *any* other outcome of your thought
> experiment.
>
> > Make it simpler for you. Infinite people RANDOMLY toss a coin
> > 3 times. Is it possible for you to toss a coin 3 times in a new
> > sequence?
> >
> > OBVIOUSLY NOT
>
> Obviously. It is perfectly possible that the *every* person that
> tossed his coin three times got heads every toss. That is a logical
> possibility and indeed that outcome isn't more or less likely than any
> other outcome.
>
> Note: The probability that your toss matches another toss on the list
> is 1. I don't dispute that --- but it is nonetheless possible that
> your outcome is not on the list.
>
> And the difference between three tosses and countably many tosses is
> relevant, too. The set of all sequences of {H,T} of length 3 is
> countable. The set of all infinite sequences of {H,T} is uncountable.

So if an infinite number of people all tossed a coin, either heads or
tails, you claim its possible to find a new undiscovered side to the
coin? And this is the exact logic you behold to ascertain the
existence of higher infinities is it not? Monte Carlo does play
cards.

So is Cantor's diag argument reducable to this.
Assume the real list is now a particular structured list we can
choose:
Real 1 : 0.1
Real 2 : 0.01
Real 3 : 0.001
...
Hence we have hyper infinities and super hyper infinities only us
graduates can comprehend, we get all numbers to infinity and change
every digit to make a new number, super duper triple looper infinity
for the super iq elite, if you don't agree you must be stupid, even if
every possible digit sequence still appears on the list of computable
numbers??

Why don't you use a suitable random generator like the digit sequence
of sqrt(2) to remove the logical absurdity of 0 probability you are
forced to introduce.

Herc
A million monkeys cooking in a million kitchens,
can one of them make pi?

Relevant Pages

  • Re: Cantors diagonal proof wrong?
    ... P(random digit sequence of length n = 1st n digits of pi) ... Countable infinity logic must be painful to ... Infinite people RANDOMLY toss a coin ... > tossed his coin three times got heads every toss. ...
    (sci.math)
  • Re: the unpredictability question
    ... >>distribution as an attribute of a single symbol. ... >>there must be an infinity of them, and for any one distribution to be ... > we toss an arbitrarily picked up coin from our infinte coin base.. ...
    (sci.math.symbolic)
  • Re: Calculus XOR Probability
    ... Hey, if you're happy with that reasoning, well, have at it. ... bizarre notions about infinity - it happens in _actual_ probability ... expected number of heads in one coin toss? ... something he's said is not total nonsense is either missing ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... It is the intended meaning of E that makes it nonsense. ... Answer: Infinity. ... expected number of heads in one coin toss? ... something he's said is not total nonsense is either missing ...
    (sci.math)