Re: how

On 4/12/2024 1:31 PM, Tom Bola wrote:

Chris M. Thomasson schrieb:
 

On 4/12/2024 7:40 AM, WM wrote:

Le 12/04/2024 à 16:02, Richard Damon a écrit :

On 4/12/24 9:45 AM, WM wrote:

>

There are no "Natural Numbers" with less than ℵo successors.

>
Self-contradiction: These successors are natural numbers but can't be
used because they can't be used up.

>
How many successors does say, 42 have?
>
Infinite!
>
How many predecessors does 3 have?
>
1->2->3->...
>
?
>
This is a finite view of an infinite process. As soon as I say three, I
am in a finite realm, so to speak.

 Every n in IN is finite but there are infinitely many n in IN.

Right. So, say I need 7 digits of precision to calculate a special deep'ish zoom into a fractal. This is finite by default, however its just a finite view of an infinite fractal process. We ca zoom in forever... Fwiw, it kind of reminds me of a stack of finite sets akin to:
{ 1 }
{ 1, 2 }
{ 1, 2, 3 }
{ 1, 2, 3, 4 }
...
One and on... Each set is finite, however there is an infinite amount of them...