novaBBS - comp.theory - Re: NO MISSING SUBSET IN {TF?}^N

NO MISSING SUBSET IN {TF?}^N

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Subject: NO MISSING SUBSET IN {TF?}^N
From: grahamco...@gmail.com (Graham Cooper)
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by: Graham Cooper - Sat, 18 Feb 2023 20:00 UTC

S is a SET of SUBSETS

S = {TF?}^N

each m n in N

m e S_n
OR
m !e S_n
OR
m e? S_n

not( m e T ) = m !e T
not( m !e T ) = m e T
not( m e? T ) = m e? T

===================

PRIMES = {1? 2 3 5 7....}
1 e? PRIMES

not( 1 e? PRIMES }
= 1 e? PRIMES

====================

Any enumeration of a powerset(N) is incomplete

let LIST(f(x y z..)) be some list of some or all of the elements of f(x y z..)

POWERSET PROOF
-----------------------------
ALL L
L = LIST( {T F}^N )
->
| {T F}^N - L | > 0

HOWEVER

EXIST L
L = LIST( {T F ?}^N)
^ {T F ?}^N = L

The Total Powerset can be listed

eg PRIMES
{1? 2 3 5 7...} e {T F ?}^N

| {T F ?}^N - {T F}^N | > 0

{T F}^N C {T F ?}^N

========================

CANTORS METHOD IS JUST

[ M_1=!S_1_1 ] ^ [ M_2=!S_2_2 ] ^ [ M_3=!S_3_3 ] ...
->
[ M_1!=S_1_1 ] ^ [ M_2!=S_2_2 ] ^ [ M_3!=S_3_3 ] ...

its a PHANTOM construction
equal to any RANDOM sequence using different permutations of S
it is non-computable

> > N <BIJECTS> {T F ?}^N
> Show the Bijection!
>
> Show me how to determine the numeric lable you are assigning to any
> arbitrary subset of your set.

N <BIJECTS> ALL_TM <BIJECTS> ALL_SUBSETS

Not only do you get ALL SUBSETS of N

1 {1 2 3}
2 {3 6? 9 12?}
3 {2 3? 5 7...}
....

you get ALL possible combinations of UNKNOWN SET MEMBERSHIP

M = CANTORS MISSING SET

M = {2 3? .. }

WHICH IS IN {TF?}^N ABOVE

http://paint3.com/powercube.gif

Re: NO MISSING SUBSET IN {TF?}^N

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Subject: Re: NO MISSING SUBSET IN {TF?}^N
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From: Rich...@Damon-Family.org (Richard Damon)
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by: Richard Damon - Sat, 18 Feb 2023 20:15 UTC

On 2/18/23 3:00 PM, Graham Cooper wrote:
> S is a SET of SUBSETS
>
> S = {TF?}^N
>
> each m n in N
>
> m e S_n
> OR
> m !e S_n
> OR
> m e? S_n
>
> not( m e T ) = m !e T
> not( m !e T ) = m e T
> not( m e? T ) = m e? T
>
> ===================
>
> eg
>
> PRIMES = {1? 2 3 5 7....}
> 1 e? PRIMES
>
> not( 1 e? PRIMES }
> =
> 1 e? PRIMES
>
> ====================
>
> Any enumeration of a powerset(N) is incomplete
>
> let LIST(f(x y z..)) be some list of some or all of the elements of f(x y z..)
>
>
> POWERSET PROOF
> -----------------------------
> ALL L
> L = LIST( {T F}^N )
> ->
> | {T F}^N - L | > 0
>
>
> HOWEVER
>
> EXIST L
> L = LIST( {T F ?}^N)
> ^
> {T F ?}^N = L
>
> The Total Powerset can be listed
>
> eg PRIMES
> {1? 2 3 5 7...} e {T F ?}^N
>
> | {T F ?}^N - {T F}^N | > 0
>
> {T F}^N C {T F ?}^N
>
> ========================
>
> CANTORS METHOD IS JUST
>
> [ M_1=!S_1_1 ] ^ [ M_2=!S_2_2 ] ^ [ M_3=!S_3_3 ] ...
> ->
> [ M_1!=S_1_1 ] ^ [ M_2!=S_2_2 ] ^ [ M_3!=S_3_3 ] ...
>
>
> its a PHANTOM construction
> equal to any RANDOM sequence using different permutations of S
> it is non-computable
>
>>> N <BIJECTS> {T F ?}^N
>> Show the Bijection!
>>
>> Show me how to determine the numeric lable you are assigning to any
>> arbitrary subset of your set.
>
>
> N <BIJECTS> ALL_TM <BIJECTS> ALL_SUBSETS
>
> Not only do you get ALL SUBSETS of N
>
> 1 {1 2 3}
> 2 {3 6? 9 12?}
> 3 {2 3? 5 7...}
> ...
>
> you get ALL possible combinations of UNKNOWN SET MEMBERSHIP

Nope, because "unknown" is not a valid membership state.

>
> M = CANTORS MISSING SET
>
> M = {2 3? .. }
>
> WHICH IS IN {TF?}^N ABOVE
>
>
>
> http://paint3.com/powercube.gif
>
>
>

You are just proving that YOUR KNOWLEDGE is in the unknown set.

I don;t think you have a real formal definition of this "Unknown
membership" critera, and it seems to just lead to contradictory statements.

Kirk to Enterprise -- beam down yeoman Rand and a six-pack.

devel / comp.theory / Re: NO MISSING SUBSET IN {TF?}^N

Subject	Author
NO MISSING SUBSET IN {TF?}^N	Graham Cooper
NO MISSING SUBSET IN {TF?}^N	Richard Damon