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:* firstname.lastname@example.org > <mailto:email@example.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/> > > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---