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

On 10/20/2024 7:17 AM, FromTheRafters wrote:

After serious thinking Richard Damon wrote :

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.

 That's it. If a proper subset results in a different cardinality, it is a finite set. If a set is not finite, it is infinite. What he doesn't like is the bijective mapping between infinitely many elements without seeing their set membership cards first. :)

>
;^D
>
{ 1, 2, 3, ... }
>
{ 1*2, 2*2, 3*2, ... }
>
{ (1*2)/2, (2*2)/2, (3*2)/2, ... }
>
WM's mind explodes? Something like this?
>
Big Trouble in Little China - Thunder blows himself up
>
https://youtu.be/A_MnyV-HH3U