Re: 2N=E

On 10/25/2024 8:54 PM, Moebius wrote:

Am 24.10.2024 um 16:37 schrieb Moebius:

Am 24.10.2024 um 16:32 schrieb Moebius:

Am 24.10.2024 um 15:59 schrieb joes:

[...]

>
Nonsense. It proves _actual_ infinity.

>
Hint:
For any nonempty set of natural numbers M:
M is infinite  iff
for each and every element m in M
there's an element m' in M such that
m' > m.
>
(Note that sets don't change.)

>
The following approach concerning "|-symbols"
might be considered
a "representation" of "potential infinity":

It seems to me that
we could also call |-symbols
numerals in base |

Rule 1:
We may construct the |-symbol |.
>
Rule 2:
Given any |-symbol
we may construct an |-symbol consisting of
the given |-symbol followed by |.
>
Rule 3:
All |-symbols have to be constructed by
applying rule 1 and rule 2
(finitely many times).

It is a bare fact that _we will not_
apply rules 1 and 2 more than finitely.many times,
since we are finite beings.
What is it to be finite or to be infinite?
Answering that has turned out to be more interesting
and more difficult than a first glance might suggest.
It also seems to me (without reading more)
that the question moves the discussion
from potential infinity to actual infinity.
I'm going to abuse the terms a little
and use 'potentially.finite' to refer to
things finite as a consequence of
the bare fact of our finitude.
Rules 1 and 2 alone describe
potentially.finite |-symbols.
What is a |-symbol?
|-instances in linear (trichotomous,transitive) order.
First and last |-instances.
For each split of the |-symbol,
a last |-instance before and a first after.
We've clarified what 'finitely.many' means,
and now I think a bit more abuse is called for,
and those are actually finite |-symbols.
With the actually finite, we get as a package deal
the actually infinite,
the not.actually.finite, such as _all_ the |-symbols.
We _don't_ get the potentially infinite,
in my abusive sense,
not for logical reasons,
but because of the bare fact of our finitude.