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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Thu, 4 Jul 2024 21:40:55 -0700
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On 7/4/2024 1:30 PM, Moebius wrote:
> Am 04.07.2024 um 22:23 schrieb Chris M. Thomasson:
> 
>> I was just thinking that infinite is infinite, 
> 
> No, it isn't.

For some reason I like to think of the density of infinity. The Natural 
numbers are not dense at all when compared to the reals...


>> there is an infinite number of natural numbers, 
> 
> Right, _countably_ infinitely many.
> 
>> there are an infinite amount of [real] numbers between say, .0000001 
>> and .00000001
> 
> _Uncountably_ infinitely many.

Okay. I get a little confused by that sometimes. Trying to count the 
reals is not possible because of all those infinite infinities that are 
embedded in them... However The naturals have no infinities between say, 
1 and 2. Make any sense to you?