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

[Tom Duff]

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/
>
>
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