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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Thu, 9 Jan 2025 17:19:13 -0800
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On 1/9/2025 5:15 PM, Moebius wrote:
> Am 09.01.2025 um 22:12 schrieb Chris M. Thomasson:
>> On 1/9/2025 8:18 AM, WM wrote:
>>> On 09.01.2025 10:56, FromTheRafters wrote:
>>>> WM explained :
>>>
>>>>> The set {1, 2, 3, ...} is smaller by one element than the set {0, 
>>>>> 1, 2, 3, ...}.
>>>>
>>>> Both sets are equal in size
>>>
>>> No. Both sets appear equal (although everybody can see that they are 
>>> not) when measured by an insufficient tool.
>>
>> { 0, 1, 2, 3, ... } = { 1 - 1, 2 - 1, 3 - 1, 4 - 1, ... }
> 
> Really? :-)
> 

Well, wrt their elements are equal to each other. Fair enough?

;^o

{ 0, 1, 2, 3, ... } = { 1 - 1, 2 - 1, 3 - 1, 4 - 1, ... }

where:

{ 0 = 1 - 1, 1 = 2 - 1, 2 = 3 - 1, 3 = 4 - 1, ... }

? Kind of okay? They both have the same number of elements.