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

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