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Topic: say I flip a coin 100 times...
Replies: 46   Last Post: Apr 18, 2005 9:42 PM

 Messages: [ Previous | Next ]
 Patricia Shanahan Posts: 4 Registered: 1/29/05
Re: say I flip a coin 100 times...
Posted: Apr 17, 2005 1:20 PM

HERC777 wrote:

> Right!
>
> So if each flipper represented a real number, and Herc
> starts flipping/making the antidiagonal (#1) at t=1, t=2,
> ...

There are two main cases:

1. Herc is flipping a fair coin, without looking at other
results. In this case, the probability of matching the first
n elements of the antidiagonal is 2^{-n}, which tends to
zero as n tends to infinity.

In this case, Herc's infinite sequence may or may not match
some other coin tosser's sequence, but it has zero
probability of being any particular sequence, including the
antidiagonal.

2. Herc is looking at the diagonal, and controlling the coin
to ensure his tosses form the antidiagonal, breaking the
assumption that the coin tosses are independent events. The
probability that Herc's first n tosses match any of the
first n sequences is zero, for all n, so the limit as n
tends to infinity is also zero.

In this case, Herc must form a new sequence, because we know
his sequence is different in at least one place from each of
the other coin tosser's sequences.

As a meta-comment, to prove countability of the set of all
coin toss result sequences it would be insufficient to find
an error in the diagonal proof. That would merely shift the
issue to being unknown. One would have to positively prove
that there exists a function F from the natural numbers into
the set of all coin toss sequences such that each coin toss
sequence is F(n) for some natural number n.

Patricia

Date Subject Author
4/12/05 HERC777
4/12/05 Jan Burse
4/12/05 HERC777
4/12/05 George Greene
4/13/05 Barb Knox
4/13/05 HERC777
4/13/05 Yajun
4/13/05 HERC777
4/13/05 Jay
4/13/05 HERC777
4/13/05 Jay
4/14/05 Yajun
4/14/05 George Greene
4/14/05 George Greene
4/13/05 Will Twentyman
4/13/05 briggs@encompasserve.org
4/13/05 briggs@encompasserve.org
4/14/05 George Greene
4/14/05 tchow@lsa.umich.edu
4/14/05 briggs@encompasserve.org
4/12/05 Tony
4/13/05 HERC777
4/13/05 ken quirici
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 tchow@lsa.umich.edu
4/13/05 HERC777
4/13/05 tchow@lsa.umich.edu
4/14/05 HERC777
4/14/05 George Greene
4/14/05 HERC777
4/15/05 tchow@lsa.umich.edu
4/15/05 tchow@lsa.umich.edu
4/16/05 George Greene
4/16/05 HERC777
4/17/05 George Greene
4/17/05 Patricia Shanahan
4/17/05 HERC777
4/18/05 Patricia Shanahan
4/17/05 tchow@lsa.umich.edu
4/18/05 HERC777
4/18/05 George Greene
4/18/05 tchow@lsa.umich.edu
4/18/05 HERC777