Re: Replacement of Cardinality

Le 31/07/2024 à 10:51, Mikko a écrit :

On 2024-07-30 14:41:15 +0000, WM said:

Growth by more than 1 is contradicting mathematics.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Note the universal quantifier.

 Irrelevant.

Mathematics is not irrelevant? ? ?

If (0, x) is a subset of (0, y), the relative quantities are clear.

 As Galilei pointed out, it is not. That one is a subset of the other
makes one look bigger but the existence of a bijection between the two
makes them look equal. Bot appearences cannot be true, so the clarity
is a hallusination.

The bijection is not true.

 However, although Galilei was happy with all infinities being equalt

Whether he was happy is irrelevant. When you claim as many natural numbers as algebraic numbers, you are a crank of mathology.
Regards, WM

there is a way out, and in fact more than one way: at least cardinals,
ordinals, and measures, perhaps something else.