Sujet : Re: All infinities are countable in ordinary mathematics
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.mathDate : 04. May 2025, 21:40:26
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <vv8jbr$2pai9$2@dont-email.me>
References : 1 2
User-Agent : Mozilla Thunderbird
On 5/4/2025 1:38 PM, Chris M. Thomasson wrote:
On 5/4/2025 6:27 AM, Julio Di Egidio wrote:
If there exist definite transfinite numbers, then their
reciprocals must be infinitesimals, not zero. Which is
good, as infinitesimals necessitate specific additional
laws, reciprocally making the transfinite sharper. And
one issue is immediately apparent: infinitesimals are
not compatible with the Archimedean principle. Ergo,
all infinities are countable in ordinary mathematics.
Try to count all of the numbers between 0 and 1, before you move onto 2. There are infinite numbers between 0 and 1, so you cannot finish before you even think about getting to two?
You could say zero, one, two, ...
But then you would not be drilling down on the infinite infinities in between them?
All infinities are countable in ordinary mathematics
Re: All infinities are countable in ordinary mathematics