[seqfan] Re: When is a sequence a list?

[Peter Luschny]

> until recently, I thought I know pretty well which sequences are lists and
which are not.

We have not had this discussion for a long time.

I do not believe that a sequence and a list are the same.

For example, I require that two sequences can be added. I do
not require that from a list. What would be the point of adding
the prime number list to Brooklyn's phone number list? All I
require from a list is that I always know whether an element
comes before or after another.

Does knowledge of a formula determine it? No. There are functions
from N to N that are not Turing machine calculable (I use that
as equivalent to "having a formula"). However, this does not
mean that they are therefore lists.

Does the use of indexing and the related determination of the
offset help us? No. Or have you ever heard of it in real life
(that is, outside of the OEIS) that somebody talks about the
offset of the natural numbers or the offset of the prime numbers?
These are practical concepts that are useful in connection with
databases but otherwise tend to be confusing.

Mathematical concepts do not live in one big pot. So what you
need to do is to look first at the structures where these
creatures live. Only by such a context do the concepts get
their meaning.

Or just get used to the general usage ...

Peter