m.a. wrote: > *Going a step further... (see below)* > ** > ----- Original Message ----- > From: "Brent Meeker" <meeke...@dslextreme.com > <mailto:meeke...@dslextreme.com>> > To: <everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>> > Sent: Wednesday, July 22, 2009 12:57 PM > Subject: Re: The seven step series > > > > > m.a. wrote: > >> Hi Brent, > >> I really appreciate the help and I hate to impose on > >> your patience but...(see below) > >> > >> ----- Original Message ----- > >> From: "Brent Meeker" <meeke...@dslextreme.com > <mailto:meeke...@dslextreme.com> > >> <mailto:meeke...@dslextreme.com>> > >> To: <everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com> > >> <mailto:everything-list@googlegroups.com>> > >> Sent: Tuesday, July 21, 2009 5:24 PM > >> Subject: Re: The seven step series > >> > >> > > >> > Take all strings of length 2 > >> > 00 01 10 11 > >> > Make two copies of each > >> > 00 00 01 01 10 10 11 11 > >> > >> > Add a 0 to the first and a 1 to the second > >> > 000 001 010 011 100 101 110 111 > >> > and you have all strings of length 3. > >> *I can see where adding 0 to the first and 1 to the second gives 000 > and > >> 001 and I think I see how you get 010 but the rest of the permutations > >> don't seem obvious to me. P-l-e-a-s-e explain, Best,* > >> ** > >> > >> > They aren't permutations. They're just sticking a 0 or 1 on the end. > One copy > > of 01 becomes 010 and the other become 011. > > *Then I assume the next step would be making two copies of each of those:* > ** > *000 **000 001 001 010 010 011 011 > 100 100 101 101 110 110 > 111 111* > ** > *...and sticking a 0 or 1 at the end:* > ** > *0000 0001 0010 0011 0100 0101 0110 0111 > 1000 1001 1010 1011 1100 1101 > 1110 1111* > ** > *and this is the binary sequence of length 4.*

Right, it's all the binary strings of length 4 > ** > *How do these translate into ordinary numerals? 1,2,3,4...* Bruno's using them to represent sets and subsets. So if we have a set {a b c} we can represent the subset {a c} by 101 and {a b} by 110, etc. That's quite different from using a binary string to represent a number in positional notation. I'll leave it to Bruno whether he wants to go into that. Brent --~--~---------~--~----~------------~-------~--~----~ 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@googlegroups.com 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 -~----------~----~----~----~------~----~------~--~---