Re: Simple enough for every reader?

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.

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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.