Re: Replacement of Cardinality

On 8/16/2024 1:38 PM, Richard Damon wrote:

On 8/16/24 2:11 PM, joes wrote:

Am Fri, 16 Aug 2024 16:59:11 +0000 schrieb WM:

Le 16/08/2024 à 18:49, joes a écrit :

Am Fri, 16 Aug 2024 16:45:29 +0000 schrieb WM:

>

It does not diminish, there are always infinitely many.

Not according to mathematics: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .

I don't see the connection.
>

 His thought process seems to be that since there is a finite spacing between all the unit fractions, you can not actually have an infinite number of them, as the sum of all the spaces would become bigger than one.
 That is just a logical fallacy, a very classical one based on the Zeno Paradox that if Achilles gives the turtle a head start, he can never pass it and beat it in a race, as every time Achilles runs to the spot where the turtle was, it has moved forward some, so we need to do another loop.
 Of course, the answer is that the numbers shrink fast enough that even though we add an infinite number of them, they only sum to a finite number.
 Each being finite doesn't mean there is a lower bound on their values (other than 0), unlike the results you get when you use logic about finite sets, where there will be a lowest value in the set.

I think you got it wrt WM's "thought" process. If we say there are infinitely many and they do tend to zero, for some reason WM thinks finite. Strange for sure. Does he understand that 1/0 is not a unit fraction?