Re: November 25 is Infinite Clause day!!

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 11/29/04 

Date: Mon, 29 Nov 2004 12:46:09 +0100

herc777@hotmail.com writes:

> Don't tell Xanthian... getting a group consensus is unmathematical, we
> have to duke it out!
>
> Barb Knox, George Green, Jesse James, John Savard, Dave B, you,
> Ullrich, Will and dozens of others have all been vocally opposed to me
> in their defence of Cantors diag proof. Now they are all silent? is
> it apathy?

In my case, yes. I haven't read your posts in a few days. I caught
George's followup today and hence this response.

What did you think? That your brilliant exposition was obviously
correct and I was too embarrassed to admit it? You're so cute.

> This is the bait :
>
>> An infinite number of people toss a coin infinite times each. Can you
>> guarantee a new sequence of Heads and Tails?
>
> Herc : no, that's silly run some simulations and extrapolate to
> infinity.
> Ghost : take the diag as in Cantor's uncountabble real proof.
> Jesse : hope they all toss heads.

No. I said that there is nothing in the statement of your problem
which is inconsistent with the outcome that they all toss heads.

Unless, of course, we interpret the probabilities involved in the
frequentist sense, in which case each of the individual sequences
should satisfy that

  lim_{n->oo} (Number of H in initial n tosses/n) = 1/2

In that case, *none* of them could toss all heads, and there's your
new sequence.

What the hell do you mean "can we guarantee a new sequence" anyway?

(1) Is there a sequence of H and T not on the list? Yes, obviously.
Use Cantor's diagonal argument. None of these arguments based on
probability are really needed, but your question is so stupidly posed
that I chose to use them instead of the standard Cantor argument.

(2) Is it necessary that, when we toss the coin, the result will be a
sequence not on the list? Obviously not, but the probability that the
result is not on the list appears to be one, near as I can figger.
That the probability is one does not make the outcome *necessary*
however.

Running simulations and "extrapolating to infinity" is a remarkable
new method of proof. What a bold reinvention of mathematics we have
here. I can't wait for the coming revolution.

In any case, by calling me "Jesse James", you have shown a subtle wit
of the sort I haven't seen since, oh, fourth grade or so. 

-- 
What you want with a hen?             What you want with a woman 
Won't cackle when she lays            when she won't do nothin' I say?  
What you want with a hen?              -- Charlie Patton,
Won't cackle when she lays               "Banty Rooster Blues"

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