[seqfan] Re: Naturals reordered: a(n)th first digit is not a(n)thdigitof S

William Keith wjk26 at drexel.edu
Tue Feb 23 22:15:16 CET 2010

 Eric Angelini wrote:
> Hello William,
> I am not sure that I understand your point:
> - are you saying that an infinite sequence is possible
>   with the rule: 
>   "Build the Z sequence using always the smallest integer 
>    not used so far"
> - or are you saying that my wording is ambiguous as it
>   would be possible to build a finite sequence _with no
>   holes_ (that is with all integers 1,2,3,4,.... n 
>   n being the last possible one (which was my intent)
> Anyway I must admit that my original phrasing is poor...
> Best,
> É.


     I mean that it seems possible to build such a sequence, but that it will not include all the natural numbers.  I am pretty sure such a sequence could be extended indefinitely (I am open to contradiction on that), but my main point is that no matter what numbers are used, the number 1023456789 will never appear in Z, because the 1023456789th digit of Z must be *something*.  So Z is not a reordering of the naturals, which I understood the original post to be claiming.

William Keith

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