Deutsch   English   Français   Italiano  
<v6et97$f608$5@dont-email.me>

View for Bookmarking (what is this?)
Look up another Usenet article

Path: ...!2.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Sun, 7 Jul 2024 13:19:50 -0700
Organization: A noiseless patient Spider
Lines: 56
Message-ID: <v6et97$f608$5@dont-email.me>
References: <tJf9P9dALSN4l2XH5vdqPbXSA7o@jntp> <v669vp$2pluv$1@dont-email.me>
 <v66kcm$2rgql$1@dont-email.me> <v66u7k$2t154$1@dont-email.me>
 <v66v36$2t7em$1@dont-email.me> <v670bh$2tdhr$1@dont-email.me>
 <v670q1$2tc0j$2@dont-email.me> <v67tgn$35707$2@dont-email.me>
 <v68s9i$3a5u1$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 7bit
Injection-Date: Sun, 07 Jul 2024 22:19:52 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="0ecdb18ed35c2abf38d5c9c78345642e";
	logging-data="497672"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX18nunsrMJT/lGTVSXlQ7DCJdJoU2Ozv65E="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:DgqEpiJWgQ38R1oe70xHt3Apua0=
Content-Language: en-US
In-Reply-To: <v68s9i$3a5u1$1@dont-email.me>
Bytes: 3137

On 7/5/2024 6:26 AM, Moebius wrote:
> Am 05.07.2024 um 06:40 schrieb Chris M. Thomasson:
>> 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...
> 
> Yeah, but this idea might be rather missleading!
> 
> Hint: The natural numbers are not dense at all when compared to the 
> rational numbers either, no?
> 
> 
> But both sets, the set of natural numbers and the set of rational 
> numbers are _countably infinite_, while the set of real numbers is 
> _uncountably infinite_
> 
>>>> 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... 
> 
> Yeah, a very good metaphor!
> 
>> However The naturals have no infinities between say, 1 and 2. Make any 
>> sense to you?
> 
> Yeah, somehow.
> 
> Still, the rational numbers are countable! (Not enough "infinite 
> infinities embedded in them"!)

Humm... Not sure about that. How many embedded infinite infinities are 
"needed" _before_ it can be deemed uncountable? Say between 0 and 1. 
There seems to be an infinite number of rationals that can fill in the 
"gap", so to speak.

0 + (1/8 + 1/8 + 1/4 + 1/2) = 1
0 + (1/16 + 1/16 + 1/8 + 1/4 + 1/2) = 1
0 + (1/16 + 1/16 + 1/8 + 2/3 + 1/3 - 1/4) = 1

These are all rational, right?