Re: Does the number of nines increase?

Liste des GroupesRevenir à s math 
Sujet : Re: Does the number of nines increase?
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.math
Date : 05. Jul 2024, 05:40:55
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v67tgn$35707$2@dont-email.me>
References : 1 2 3 4 5 6 7
User-Agent : Mozilla Thunderbird
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?

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