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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: All infinities are countable in ordinary mathematics
Date: Sun, 4 May 2025 13:40:26 -0700
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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?