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

On 10/20/2024 3:40 AM, WM wrote:

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.

It is my claim that
infinitely.many exchanges in an infinite set
can result in the loss of one of them.
1 is not infinite.

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.

A finite set can be ordered such that
each subset holds its top and bottom or is empty.
An infinite set is not finite.
∀n ∈ ℕ:
finite {2,4,6,...,2n}
finite {1,2,3,4,5,6,...,2n}
infinite {2,4,6,...}
infinite {1,2,3,4,5,6,...}