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From: joes <noreply@example.org>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Fri, 4 Jul 2025 11:18:50 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Fri, 04 Jul 2025 12:15:16 +0200 schrieb WM:
> On 04.07.2025 10:38, joes wrote:
>> Am Thu, 03 Jul 2025 21:10:39 +0200 schrieb WM:
>>> On 03.07.2025 16:12, joes wrote:
>>>> Am Thu, 03 Jul 2025 15:08:25 +0200 schrieb WM:
>>>
>>>>> The rule of subset proves that every proper subset has fewer
>>>>> elements
>>>> No such rule for infinite sets.
>>> For all sets.
>> No, this is not an accepted theorem of mainstream mathematics.
> But it is correct. See the last paragraph. Can you contradict it?
It is incorrect: infinite sets have subsets of the same cardinality.

>>>>> than its superset. So there are more natural numbers than prime
>>>>> numbers,
>>>> No, you can number the primes.
>>> Yes, there are only few known primes.
>> ...you can enumerate them in the sense of a bijection to N: there is a
>> first prime, a second and so on for every natural, which is infinitely
>> many.
> I mentioned the *known* primes.
I didn't, and you didn't the first time. I am aware that we don't know all
primes, but you can't mean that. There aren't more naturals than primes,
one doesn't run out of primes when counting them.

>>>>> The rule of construction yields the number of integers |Z| = 2|N| +
>>>>> 1 and the number of fractions |Q| = 2|N|^2 + 1.
>>>> Those numbers are equal.
>>> Only for cranks. In mathematics we use the limit. For every large
>>> enough interval the even numbers are half as many as the natural
>>> numbers. This does never change. Consequently it holds in the limit
>>> for infinite sets.
>> And half of infinity is still infinite.
> That does not change the correct mathematics: For every interval [0, 2n]
> there are half as many even numbers as natural numbers. That is true
> also in the limit.
That is what I said.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.