[seqfan] Re: Two "dumb" sequences and a question

[Ali Sada]

 Thank you all for the informative responses. And Tom is right. I didn't intend to submit these sequences. I am sorry for not making this clear. 
I just wanted to understand how logical structures are spontaneously generated from a few simple rules and how these structures normally prevent the creation of paradoxical sets. I would really appreciate it if you could share with me materials on set theory (for non-mathematicians). 

On another note, I respectfully disagree with Brendan. "Useless" sequences might be a burden on the OEIS editors, but I don't think they would harm the efficiency of the OEIS search function. How many milliseconds would a thousand of these sequences add to the search time? And I am a Hardy's fan. I don't think "useless" is a bad word at all when it comes to mathematics! 



Best,
Ali 


    On Thursday, December 1, 2022 at 03:26:29 AM GMT+1, Joseph Myers <jsm at polyomino.org.uk> wrote:  
 
 And we do in fact already have A053873 and A053169.

-- 
Joseph S. Myers
jsm at polyomino.org.uk

On Wed, 30 Nov 2022, Tom Duff wrote:

> I don't think Ali Sada seriously wants to add these sequences. He's trying
> to understand an OEIS-driven version of Russell's paradox. The resolution
> of the paradox is that not everything you claim is a sequence really is a
> valid sequence as far as the OEIS is concerned, just as in ZF, the rules of
> set construction preclude the Russell's paradox "set" from being
> constructed. OEIS's rules aren't as rigorous as ZF's, because our idea of
> what's a submittable sequence is an evolving thing.
> 
> The point of Russell's paradox is that a wild-west attitude to set theory
> (i.e. that the objects satisfying any predicate at all define a set) is
> just asking for trouble.
> 
> On Wed, Nov 30, 2022 at 5:55 PM Frank Adams-watters via SeqFan <
> seqfan at list.seqfan.eu> wrote:
> 
> > Another problem is that the content depends on the current state of our
> > knowledge. This is unacceptable.
> >
> > Franklin T. Adams-Watters
> >
> >
> > -----Original Message-----
> > From: Brendan McKay via SeqFan <seqfan at list.seqfan.eu>
> > To: seqfan at list.seqfan.eu
> > Cc: Brendan McKay <Brendan.McKay at anu.edu.au>
> > Sent: Wed, Nov 30, 2022 7:07 pm
> > Subject: [seqfan] Re: Two "dumb" sequences and a question
> >
> > This is like the "all numbers are interesting" proof: If some numbers
> > are not
> > interesting, then there is a smallest non-interesting number, which is
> > clearly
> > an interesting property.
> >
> > Regardless, I hope that neither sequence is added to OEIS. The value of
> > OEIS
> > as a research tool is diluted every time useless made-up sequences are
> > added.
> >
> > Brendan.
> >
> > On 30/11/2022 10:58 pm, Ali Sada via SeqFan wrote:
> > > Hi everyone,
> > >
> > > Please consider the two sequences below:
> > >
> > > 1) Sequence AX contains all OEIS sequences where the A number is a term
> > in the sequence itself. For example, A000027 since 27 is a positive integer.
> > >
> > > 2) Sequence AY contains all OEIS sequences where either:
> > > a) the A number is not a term in the sequence (e.g., A000040, since 40
> > is not a prime number),
> > > or
> > > b) we don’t know if the A number is a term in the sequence or not (e.g.,
> > A329697).
> > >
> > > The question here is: Where should the number Y go? If we put it in
> > sequence AY, then we know where it belongs and that contradicts the
> > definition of AY.
> > > Also, it couldn’t be part of AX because Y is not a term of AY.
> > >
> > > I’m trying to have some basic understanding of set theory and I would
> > really appreciate your feedback.
> > >
> > > Best,
> > >
> > > Ali
> > >
> > >
> > > --
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> > --
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> >
> 
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