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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: Sat, 14 Dec 2024 14:20:51 -0800
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On 12/14/2024 3:10 AM, joes wrote:
> Am Thu, 12 Dec 2024 23:03:51 +0100 schrieb WM:
>> On 12.12.2024 18:29, Jeff Barnett wrote:
>>> On 12/12/2024 6:59 AM, joes wrote:
>>>> Am Tue, 10 Dec 2024 18:01:04 +0100 schrieb WM:
>>>>> On 10.12.2024 13:19, Richard Damon wrote:
>>>>>
>>>>>> The pairing is between TWO sets, not the members of a set with
>>>>>> itself.
>>>>> The pairing is between the elements. Otherwise you could pair R and Q
>>>>> by simply claiming it.
>>>>> "The infinite sequence thus defined has the peculiar property to
>>>>> contain the positive rational numbers completely, and each of them
>>>>> only once at a determined place." [Cantor] Note the numbers, not the
>>>>> set.
>>>> What Richard meant: do not confuse the set being mapped with the one
>>>> being mapped onto.
>>> But that's sort of what mappings are for! Aren't they?
>> Dedekind maps the elements of a subset to the elements of its superset.
>> Same do I.
> YOU try to map N onto itself.
> 

Is this cheating?


{ 1 + 0, 2 + 0, 3 + 0, ... }

lol.