Re: Replacement of Cardinality

Am Sun, 25 Aug 2024 19:47:46 +0000 schrieb WM:

Le 24/08/2024 à 19:06, Richard Damon a écrit :
 

I guess by your finite logic, Achilles can't pass the tortoise,

 
Achilles and the tortoise run a race. The tortoise gets a start and the
race begins (state 0). When Achilles reaches this point, the tortoise
has advanced further already (state 1). When Achilles reaches that
point, the tortoise has advanced again (state 2). And so on (states 3,
4, 5, ...). Since Achilles runs much faster than the tortoise, he will
overtake (state ), but only after infinitely many finitely indexed
states of the described kind. Their number must be completed.

How is this accomplished? How would this be prevented?

Otherwise
Achilles will not overtake. But there must not be a last visible
finitely indexed state.

must = can?

(The last 1000 states Achilles remembers have indices much smaller than

[Assuming at the point of overtaking]
How are these even defined there?

.) This can only be realized by means of dark states.

According to set theory, all states can be put in bijection with all
natural numbers. This is impossible as completeness and well-order
require a last mark.

Why? What do you think of as (in)complete?

The three notions "all" and "infinite" and
"well-ordered" do not match. This dilemma can only be solved by
refraining from well-order of the set Y of dark-numbered states.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.