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

WM was thinking very hard :

On 20.10.2024 00:08, Jim Burns wrote:

On 10/19/2024 2:28 PM, WM wrote:

>

>
The contradiction is independent of infinity.
It is your claim that

 infinitely.many exchanges in an infinite set
(vanishing Bob)

>
Every exchange is _one_ lossless exchange.

 

exchanging two objects
can result in the loss of one of them.

 I fixed that for you.

>
It is nonsense like:
∀n ∈ ℕ: |{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2
but |{2, 4, 6, ...}|/|{1, 2, 3, 4, 5, 6, ...} = 1.

You made some typos here. You left out a couple of "|" for the cardinalities.
Plus, how do you define division on cardinalities -- especially the infinite ones?