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

On 1/14/25 4:07 AM, WM wrote:

On 13.01.2025 20:31, Jim Burns wrote:

On 1/13/2025 12:17 PM, WM wrote:

 

Doubling of all n
deletes the odd numbers
but cannot change the number of numbers,

>
ℕ is the set of finite ordinals.
>
There is no finite set larger than ℕ
thus ℕ is infinite.
There is no infinite set smaller than ℕ

 The set of prime numbers is smaller than ℕ but appears infinite too because all sets with more than a definable number of numbers appear infinite.

The set of prime number is the same size as N, because we can make a one-to-one mapping between them.
EVERY Natural Number is "Definable", so any set which can be one-to-one mapped to the Natural Number *IS* (not just appears) infinite.
Your stupidity just keeps you from understanding this basic truth.

>
𝔼 is the set of even finite ordinals.
There is no finite set larger than 𝔼
thus 𝔼 is infinite
𝔼 ⊆ ℕ
#𝔼 ≤ #ℕ
There is no infinite set smaller than ℕ
#𝔼 ≥ #ℕ

 That is obviously wrong.

No, *YOU* are obviously wrong, and too stupid to understand it.

 

therefore creates even numbers.
They do not fit below ω.

>
No.
They fit below ω

 In completed infinity all available places are occupied.
∀n ∈ ℕ: 2n > n. All numbers are doubled. Their number remains the same (not only the cardinality, but the reality). Half of all are deleted. Half are new.

And WM proves his stupdity by not knowing how logic works.
Your logic is based on the lies that come out of the darkness of your ignorance, and you admit that you logic isn't based on actual definable facts, just your own imagination.

 

A step is never from finite to infinite.
Therefore, a step never crosses ω
Therefore, a sum never crosses ω
Therefore, a product never crosses ω
Therefore, a power never crosses ω

 All that is true in potential infinity, however it is wrong in completed infinity.

Nope, the problem is your logic doesn't work in the "completed" infinity. I guess you didn't really understand the words you read about it.

 Regards, WM