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

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Patricia Shanahan

Posts: 4
Registered: 1/29/05
Re: say I flip a coin 100 times...
Posted: Apr 18, 2005 12:35 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

HERC777 wrote:
>>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

>
>
> not only has this conclusion been proven wrong it is a non sequitur.
> as n tends to infinity, the sequence is different at the nth place.
>
> 0.9.. is different to 0.9 at the 2nd place.
> 0.9.. is different to 0.99 at the 3rd place.
>
> 0.9.. =/= 0.99...9 (n 9s) forall n. so the limit as n tends to infinity
> is they are also unequal.


From this and other remarks you have made, I think we are
using different definitions of being in an infinite list.
Here are a couple of candidate definitions:

========================================================

Definition 1

If x is an element of a set X, and L=(l_0,l_1,...) is an
ordered list of elements of X, then x is in L if, and only
if, there exists a natural number n such that x=l_n.

========================================================

Definition 2

If x is an element of a set X, and L=(l_0,l_1,...) is an
ordered list of elements of X, then x is in L if, and only
if, at least one of the following two conditions is met:

Either

there exists a natural number n such that x=l_n

or

x is an infinite length sequence of symbols from some
alphabet A, and for every natural number m greater than some
natural number m0, if x_{1..m} is the length m prefix of x,
there exists a natural number n such x_{1..m}=l_n

========================================================

If you agree with one of these definitions, please indicate
which. If you agree with neither, please state your own.

Definitions matter. According to definition 1, 0.9.. is not
in the list (0.9, 0.99, 0.999, ...). According to definition
2, it is.

Patricia




Date Subject Author
4/12/05
Read say I flip a coin 100 times...
HERC777
4/12/05
Read Re: say I flip a coin 100 times...
Jan Burse
4/12/05
Read Re: say I flip a coin 100 times...
HERC777
4/12/05
Read Re: say I flip a coin 100 times...
George Greene
4/13/05
Read Re: say I flip a coin 100 times...
Glenn C. Rhoads
4/13/05
Read Re: say I flip a coin 100 times...
Barb Knox
4/13/05
Read Re: say I flip a coin 100 times...
HERC777
4/13/05
Read Re: say I flip a coin 100 times...
Yajun
4/13/05
Read Re: say I flip a coin 100 times...
HERC777
4/13/05
Read Re: say I flip a coin 100 times...
Jay
4/13/05
Read Re: say I flip a coin 100 times...
HERC777
4/13/05
Read Re: say I flip a coin 100 times...
Jay
4/14/05
Read Re: say I flip a coin 100 times...
Yajun
4/14/05
Read Re: say I flip a coin 100 times...
George Greene
4/14/05
Read Re: say I flip a coin 100 times...
George Greene
4/13/05
Read Re: say I flip a coin 100 times...
Will Twentyman
4/13/05
Read Re: say I flip a coin 100 times...
briggs@encompasserve.org
4/13/05
Read Re: say I flip a coin 100 times...
briggs@encompasserve.org
4/14/05
Read Re: say I flip a coin 100 times...
George Greene
4/14/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/14/05
Read Re: say I flip a coin 100 times...
briggs@encompasserve.org
4/12/05
Read Re: say I flip a coin 100 times...
Tony
4/13/05
Read Re: say I flip a coin 100 times...
HERC777
4/13/05
Read Re: say I flip a coin 100 times...
ken quirici
4/13/05
Read Re: say I flip a coin 100 times...
Ralph Hartley
4/13/05
Read Re: say I flip a coin 100 times...
Robert Low
4/13/05
Read Re: say I flip a coin 100 times...
Ralph Hartley
4/13/05
Read Re: say I flip a coin 100 times...
Robert Low
4/13/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/13/05
Read Re: say I flip a coin 100 times...
HERC777
4/13/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/14/05
Read Re: say I flip a coin 100 times...
HERC777
4/14/05
Read Re: say I flip a coin 100 times...
George Greene
4/14/05
Read Re: say I flip a coin 100 times...
HERC777
4/15/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/15/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/16/05
Read Re: say I flip a coin 100 times...
George Greene
4/16/05
Read Re: say I flip a coin 100 times...
HERC777
4/17/05
Read Re: say I flip a coin 100 times...
George Greene
4/17/05
Read Re: say I flip a coin 100 times...
Patricia Shanahan
4/17/05
Read Re: say I flip a coin 100 times...
HERC777
4/18/05
Read Re: say I flip a coin 100 times...
Patricia Shanahan
4/17/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/18/05
Read Re: say I flip a coin 100 times...
HERC777
4/18/05
Read Re: say I flip a coin 100 times...
George Greene
4/18/05
Read Re: say I flip a coin 100 times...
tchow@lsa.umich.edu
4/18/05
Read Re: say I flip a coin 100 times...
HERC777

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