m.a. wrote:
> *Going a step further... (see below)*
> **
> ----- Original Message -----
> From: "Brent Meeker" <meekerdb.domain.name.hidden
> <mailto:meekerdb.domain.name.hidden>>
> To: <everything-list.domain.name.hidden
> <mailto:everything-list.domain.name.hidden>>
> 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" <meekerdb.domain.name.hidden
> <mailto:meekerdb.domain.name.hidden>
> >> <mailto:meekerdb.domain.name.hidden>>
> >> To: <everything-list.domain.name.hidden
> <mailto:everything-list.domain.name.hidden>
> >> <mailto:everything-list.domain.name.hidden>>
> >> 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 00 to the first and a 01 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
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Received on Wed Jul 22 2009 - 20:49:24 PDT