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

On 10/20/24 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.

>

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.
 Regards, WM
 

Right, but
|{2, 4, 6, ...}| is Aleph_0, as is |{1, 2, 3, 4, 5, 6, ...}|
Which is a value you have admitted your mathematics doesn't have.
You have admitted that your "actual infinity" isn't actually infinite, and just a term used to lie.
I(nfinity isn't just "really big numbers" like you want to treat it, but a set of numbers with DIFFERENT properties from the finite.