Re: The Consise Cantor Disproof


HERC777 wrote:
> For some reason people have difficulty
> accepting the use of Monte Carlo
> simulations in Maths proofs.

That reason would be "because they are completely
irrelevant, unless you are doing a proof ABOUT
Monte Carlo simulations". There are counting and
probabilistic arguments made in a lot of proofs,
and nobody has any trouble accepting them as long
as the prover KNOWS WHAT HE'S DOING. Which you don't.


>
> According to George, if you set the digits
> of a real number to random
> 0s and 1s, 0.0000000.... or 0.1111111... are just as likely as
> 0.00110101010111010...!
>
> Well this is nonsense,

You are SO COMPLETELY FULL OF ***.

EVERY OUTCOME IS EQUALLY LIKELY, IF it's random!
That's what you MEANT by random! Of cousre, this
kind of uniform randomness IS NOT EVEN ACHIEVABLE
over an infinite domain, but, you being stupid, you
wouldn't even know THAT much.

Why don't you just take it down to the finite usual
case of 2x6, of two dice, instead of trying to be
oo x 2, an infinite bit-string (for which probability
is meaningless ANYhow). There are THIRTY-SIX possible
outcomes. Either die could come up any of 6 ways.
EVERY OUTCOME IS EQUALLY likely (it has probability
1/36). THAT IS ALL.

> its not what happens when you program computers,

It IS SO TOO what happens when you program computers,
IF YOU ACTUALLY KNOW how to program a random number
generator. Of course, since your random number generator
would have TO BE A FINITE program, there is in fact NO WAY
to make a finitary human-designed computer produce true
uniform randomness OVER AN INFINITE bit-string. But that's
what you CLAIMED that YOUR "random" function was capable of
doing. But why we are discussing this AT ALL is a MYSTERY
since it has ABSOLUTELY NOTHING to do with anti-diagonalization.
ANY denumerable list of denumerably-wide bit-strings can be
anti-diagonalized. ANY LIST WHATSOEVER. It DOESN'T FUCKING
MATTER WHAT is on the list, OR how it was generated! IF
the list EXISTS, THEN its anti-diagonal MUST exist as well!

> and its trivial to disprove.

It's IMPOSSIBLE to disprove, ESPECIALLY by anybody
as ignorant as you.

>
> Take a list of such numbers..
>
> 0.0010101110..
> 0.0111010101..
> 0.1110101010..
> 0.0011010101..
> 0.1111000101..
> ..
>
> The probability that the 1st digits are all 0s is 0! Its practically
> impossible!

The probability that the 1st digits are
EXACTLY WHAT THEY ARE ON YOUR LIST
is *ALSO* ZERO, DUMBASS! ALL these probabilities
are infinitesimal! If you generate ANY infinitely-
long RANDOM bit-string whatsoever, the probability
that it WOULD be EXACTLY what it was is 2^(oo) WHICH
IS *ZERO*, DIP***!

The WHOLE CONCEPT of "probability" in this context is
MEANINGLESS! You need a WHOLE NEW TAKE on it JUST TO
GET STARTED! You need new AXIOMS that YOU PERSONALLY
have never been within SNIFFING distance of!

.