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Topic: natural numbers as pseudocircles
Replies: 1   Last Post: Feb 4, 2014 9:42 PM

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fom

Posts: 1,969
Registered: 12/4/12
Re: natural numbers as pseudocircles
Posted: Feb 4, 2014 9:42 PM
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On 2/4/2014 8:17 PM, fom wrote:


Well, that is a little embarrassing. I
argued elsewhere for interpreting an
arithmetic error.

1/31 =/= 4/128

But, this is actually better. Only 3 is
a limit point in the convergence to 2.
And, embeddings into minimal Hausdorff
spaces are based on single-point
compactifications.


>
> The second sequence is
>
> 0 < 1/128 < 2/128 < 3/128 < 4/128 < 5/128 < 1/18 < 1/16 < 1/9
>
> Its partition will be,
>
>
> interval_1 :=> { ..., 131 }
> interval_2 :=> { 127, ..., 67 } [13 primes] [length: 60] [gap: 4]
> interval_3 :=> { 61, ..., 43 } [5 primes] [length: 18] [gap: 6]
> interval_4 :=> { 41, 37 } [2 primes] [length: 4] [gap: 2]
> interval_5 :=> { 31, 29 } [2 primes] [length: 3] [gap: 6]
> interval_6 :=> { 23, 19 } [2 primes] [length: 4] [gap: 6]
> interval_7 :=> { 17 } [1 prime] [length: 0] [gap: 2]
> interval_8 :=> { 13, 11 } [2 primes] [length: 2] [gap: 4]
>
> residual :=> { 7, 5, 3, 2 } [4 primes] [length: 5] [gap: 4]
> omitted :=> {} [0 primes] [length: null] [gap: null]
>







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