Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/9/24 5:28 AM, WM wrote:

On 08.10.2024 20:01, Richard Damon wrote:

On 10/8/24 11:26 AM, WM wrote:

 

But after the visble natural numbers the dark domain comes, and that is what prevents to see the end (which is dark too).

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Where?
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The "visible" numbers, per you definition are ALL the numbers, as all of them can be used individually and are selectable.

 Wrong. Every visible number has infinitely many successors. Therefore there are infinitely many successors beyond every visible number. Otherwise there was a visible number with less successors.

Right, every visible numbers has an infinitely many VISIBLE successors, thus no last one.

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Thus, there aren't any left to be dark, except the ones that don't actually exist.
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That shows my point. Infinite sets can be moved. 0.999...999 moved gives
9.99...9990.

You have not indicated what this notation means. Where does the zero come
from?

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The last natural index has lost its 9 by shifting to the left-hand side. Hence there is nothing remaining.

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How did it "lose" it,

 By shifting to the left-hand side.

but it had no end, or it wasn't infinite.
Your problem seems to be that you refuse to understand what "infinite" means.

 Regards, WM