Re: Replacement of Cardinality

On 8/11/2024 8:29 AM, WM wrote:

Le 10/08/2024 à 19:28, Jim Burns a écrit :

On 8/10/2024 11:54 AM, WM wrote:

Le 09/08/2024 à 02:32, Jim Burns a écrit :

Surely, a lawyer wouldn't think that
"Boom! Here's the conclusion"
is an _argument_ ?

>
∀n ∈ ℕ: 1/n - 1/(n+1) > 0

<place for argument>

If an interval contains unit fractions,
then it contains a first one.
>

Therefore
there can only be a single first unit fraction.

>
No one has said there are two first unit.fractions.
What forbids zero first unit.fractions?

<place for argument>

The existence of unit frations enforces
one or more first unit fractions.
>

What causes an exception: nₓ ∈ ℕ without ⅟(nₓ+1) ?

>
The end of the positivee axis.

∀n ∈ ℕ: 1/n - 1/(n+1) > 0

∀n ∈ ℕ: 1/n > 1/(n+1) > 0
Each positive unit fraction is not
the first positive unit fraction.
What causes an exception: nₓ ∈ ℕ:
⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?