Each binary string of length n has two possible continuations of  length 
n+1, one of them by appending a 0 and one of them by appending a 1.  So 
to get all binary strings of length n+1 take each string of length n, 
make two copies, to one copy append a 0 and to the other copy append a 1.

Brent

m.a. wrote:
> Hi Bruno,
>                    I'm not clear on the sentence in bold below, 
> especially the word "correspondingly". The example of Mister X only 
> confuses me more. Could you please give some simple examples? Thanks,
>                                                                     
>                                                                     
>                                                                     
>                                                                     
>         marty a.
>  
>  
>
>     ----- Original Message -----
>     *From:* Bruno Marchal <mailto:marc...@ulb.ac.be>
>     *To:* everything-list@googlegroups.com
>     <mailto:everything-list@googlegroups.com>
>     *Sent:* Monday, July 20, 2009 3:17 PM
>     *Subject:* Re: The seven step series
>
>
>     On 20 Jul 2009, at 15:34, m.a. wrote:
>
>>     And then we have seen that such cardinal was given by 2^n. 
>     You can see this directly by seeing that adding an element in a
>     set, double the number of subset, due to the dichotomic choice in
>     creating a subset "placing or not placing" the new element in the
>     subset.
>      
>     *Likewise with the strings. If you have already all strings of
>     length n, you get all the strings of length n+1, by doubling them
>     and adding zero or one correspondingly.*
>      
>     This is also illustrated by the iterated self-duplication W, M.
>     Mister X is cut and paste in two rooms containing each a box, in
>     which there is a paper with zero on it, in room W, and 1 on it in
>     room M. After the experience, the 'Mister X' coming out from room
>     W wrote 0 in his diary, and the 'Mister X' coming out from room M
>     wrote 1 in his diary. And then they redo each, the experiment. The
>     Mister-X with-0-in-his-diary redoes it, and gives a Mister-X
>     with-0-in-his-diary coming out from room W, and adding 0 in its
>     diary and a  Mister-X with-0-in-his-diary coming out from room M,
>     adding 1 in its diary: they have the stories 
>
>      
>     Bruno
>
>
>
>     http://iridia.ulb.ac.be/~marchal/
>     <http://iridia.ulb.ac.be/%7Emarchal/>
>
>
>
>
>
>     >


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