Re: Simple enough for every reader?

On 18.05.2025 08:27, Chris M. Thomasson wrote:

On 5/17/2025 11:20 PM, Chris M. Thomasson wrote:

On 5/17/2025 12:06 PM, FromTheRafters wrote:

After serious thinking Chris M. Thomasson wrote :

On 5/17/2025 10:35 AM, WM wrote:

Exciting. Many readers claim(ed) that all natural numbers could be used as individuals. Further this would be a precondition for countability of infinite sets.

>
Show me a dark natural number?

Take the greatest number that you can express. All greater numbers are dark yet. Double your greatest number and express the result. Then you see a hitherto dark number. Of course it is no longer dark. But infinitely many numbers remain dark

We are building a natural number digit by digit using random rolls, the first roll needs to be higher that zero... Fair enough? They will all be natural numbers, right?

Of course. All will be natural numbers. It is a potentially infinite set, {1, 2, 3, ..., n}, always finite but without a upper bound, followed by an infinite set of dark numbers, infinitely many of which will remain dark forever.

 So, how could my process "break" when the natural numbers are infinite any at any step of the process,

Your process will not break. One after one the dark numbers will become visible. Nevertheless almost all natural numbers will remain dark. The stock is incredibly large. There are numbers like ω/2 or ω/10 which you will never touch. For every defined n ∈ ℕ: ω/n is larger than you will every reach, how long ever you will increase your visible numbers. Compared to ω the defined numbers are infinitesimal.
Regards, WM