On 5/3/2024 4:31 PM, WM wrote:
Le 03/05/2024 à 21:32, Jim Burns a écrit :
On 5/3/2024 9:57 AM, WM wrote:
It is the idea that infinite sets are fixed
such that no element can be added or removed.
It is the idea that
the natural numbers reach immediately from 0 until ω
Each number which CAN be counted.to from 0
is before
ℵ₀.many numbers which CAN be counted.to from 0
>
If all could be counted to,
they would not remain after every counted number.
1.
From each number n which CAN be counted.to
the numbers which CAN be counted.to reach immediately
more.than.1 from n to n+2
None of these immediate more.than.1 numbers remain
after every number n which CAN be counted.to.
The meaning of (1.) depends upon
'n' NOT being
the true name of any number which CAN be counted.to,
the way that "Rumpelstiltskin" is the true name of
a certain straw.into.gold.spinner.
An analogy better than "name" is "pronoun"
'n' is more like a pronoun than a name.
"It is a natural number", etc.
Variable.names are a big improvement over pronouns
because, in every natural language I'm aware of,
there are no more than a handful of pronouns,
used with many handfuls of referents, and
their distinct referents are kept distinct
by context, AKA, figuring.it.out.
Even if the figuring.out doesn't fail, a lot of work.
The expression
| x < y and y < z implies x < z
|
is a big improvement in clarity over
a paragraph of muddle with three pronouns.
x y z act like pronouns, though.
2.
From each number n which CAN be counted.to
the numbers which CAN be counted.to reach immediately
more.than.2 from n to n+3
None of these immediate more.than.3 numbers remain
after every number n which CAN be counted.to.
3.
From each number n which CAN be counted.to
the numbers which CAN be counted.to reach immediately
more.than.3 from n to n+4
None of these immediate more.than.3 numbers remain
after every number n which CAN be counted.to.
...
k.
From each number n which CAN be counted.to
the numbers which CAN be counted.to reach immediately
more.than.k from n to n+k+1
None of these immediate more.than.k numbers remain
after every number n which CAN be counted.to.
...
If all could be counted to,
they would not remain after every counted number.
From each number n which CAN be counted.to
for each number k which CAN be counted.to
more.than.k numbers which CAN be counted.to
can be reached immediately
from n to n+k+1
None of these immediate more.than.k numbers remain
after every number n which CAN be counted.to.
V
Re: V