Sujet : Re: Replacement of Cardinality
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.logic sci.mathDate : 11. Aug 2024, 18:56:28
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <35d8c0a1-dab3-4c15-8f24-068e8200cb07@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
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 ?
…