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

[Allan Wechsler]

You don't have to go that far to create a sequence that is "paradoxical" in
this sense. Suppose we try to add to OEIS a sequence -- say, A400000 --
whose title is "List of nonnegative integers not included in A400000", or
more simply, "Complement of A400000". Now we can't decide whether *any *integer
belongs there. For example, should 17 go in? If the answer is yes, then it
shouldn't, and if the answer is no, then it should.

I think for the moment all we have to say is that there is a kind of
noxious self-reference that makes a sequence unsuitable for inclusion in
OEIS, and doing any kind of math with sequence numbers is a warning sign of
this.

Under that approach, the answer to Ali's actual question is, "This question
won't arise, because that kind of sequence is not suitable for inclusion in
OEIS."

On Wed, Nov 30, 2022 at 8:32 AM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
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
>
>
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