Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/3/24 6:10 AM, WM wrote:

On 03.12.2024 11:03, Mikko wrote:
 

I understand mathematics

 Hardly, though you may have the impression.
 Proof: You cannot understand that the function
f(10n) = n from D = {10n | n ∈ ℕ} to ℕ = {1, 2, 3, ...} is not a bijection because for every initial segment {1, 2, 3, ..., n} of ℕ there are too few numbers of the form 10n that can be paired with numbers n. Since ℕ is the union (or the limit) of the sequence of initial segments {1, 2, 3, ..., n}, there are too few numbers of the form 10n in ℕ that can be paired with numbers n.
 Regards, WM
 

Except that isn't the definition of the set ℕ, so the proof is based on a false premise.
Sorry, you are just showing that your Naive Mathematics is based on inconsistent presumptions that break it when you try to apply it to infinities.
Of course, that has been your problem all along, that you logic system, as has your brain, has been exploded by the inconsistencies that it is built on.
You just reject the properly built Mathematics, because it requires actually understanding it, and shows to be true a few statements you don't like. Your preferences don't define Mathematics, so you are just stuck being wrong.