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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Fri, 10 Jan 2025 07:41:24 -0500
Organization: i2pn2 (i2pn.org)
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On 1/9/25 11:48 AM, WM wrote:
> On 09.01.2025 13:17, Richard Damon wrote:
>> On 1/9/25 4:38 AM, WM wrote:
>>> On 09.01.2025 00:45, joes wrote:
>>>> Am Wed, 08 Jan 2025 23:06:27 +0100 schrieb WM:
>>>
>>>>> The set {1, 2, 3, ...} is smaller by one element than the set {0, 
>>>>> 1, 2,
>>>>> 3, ...}. Proof: {0, 1, 2, 3, ...} \ {1, 2, 3, ...} = {0}. Cardinality
>>>>> cannot describe this difference because it covers only mappings of
>>>>> elements which have almost all elements as successors.
>>>> You can't talk about size without using |abs|.
>>>
>>> I can and I do. And everybody understands it in case of subsets. This 
>>> proves, in this special case (and more is not required), that 
>>> Cantor's size is only a qualitative measure, not a quantitative one.
> 
>> Sorry it *IS* true,
> 
> It is true that {1, 2, 3, ...} is a set and {0, 1, 2, 3, ...} is a 
> greater set. Your hysteric moaning cannot change that.
> 
> Regards, WM
> 

No, one may be the proper subset of the other, but it turns out that due 
to the way that infinity works, they are both are the same size.

"Greater" doesn't apply to set that are of the same order of infinity in 
size.

Sorry, you are just stuck in your own ignorance, that tries to use 
things it claims can't exist, and thus blows itself up in its own 
self-contradictions.