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

On 1/8/25 4:50 PM, WM wrote:

On 08.01.2025 18:32, FromTheRafters wrote:

WM explained :

On 08.01.2025 12:04, FromTheRafters wrote:

WM formulated on Wednesday :

>

If ω exists, then ω-1 exists.

>
Wrong.

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A set like ℕ has a fixed number of elements. If ω-1 does not exist, what is the fixed border of existence?

>
Who says that there has to be a  fixed border of existence?

 According to set theory every set has a fixed set of elements, not more and not less.

Right, but that doesn't mean it has a border. You just don't understand what infinity means.

 

Omega is a limit ordinal not a successor.

 But the natural numbers are invariable. For every n, there is n+1 which is not created but simply exists.

Right, and thus there can't be a "last" natural number, that is just a property of the infinite.
That also means there is no smallest unit fraction, and all you arguments about that are just your own delusions showing your ignorance.

 Regards, WM