Each binary string of length n has two possible continuations of length
n+1, one of them by appending a 00 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:marchal.domain.name.hidden>
> *To:* everything-list.domain.name.hidden
> <mailto:everything-list.domain.name.hidden>
> *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 01 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/>
>
>
>
>
>
> >
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list.domain.name.hidden
To unsubscribe from this group, send email to everything-list+unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---
Received on Tue Jul 21 2009 - 12:57:59 PDT