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

On 1/5/25 12:21 PM, WM wrote:

On 05.01.2025 13:45, Richard Damon wrote:

On 1/5/25 5:40 AM, WM wrote:

 

For all FISONs:|ℕ \ {1, 2, 3, ..., n}| = ℵo.
That means there is no exception.
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Just like every natural number is finite,
but the set of *ALL* of them is infinite, each FISON is finite,

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Not only finite but below 1 % of |ℕ|.

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So? Until you can handle *ALL* of them together, your claim is just a lie about the whole.

 As Cantor said actual infinity, for instance omegas and alephs and ℕ are fixed quantities. The set ℕ is invariable. But all finite initial segments of natural numbers FISONs {1, 2, 3, ..., n} cover less than 1 % of ℕ. Proof: {1, 2, 3, ..., 100n} is less than ℕ. That means the set of FISONs will never cover ℕ, nor will its union reach the invariable quantity. The set of FISONs is only potentially infinite, not a fixed quantity but growing over all finite bounds.
 Regards, WM
 

THey are invariable, but infinite. No finite entity approaches the infinite.
THe fact that you think it should, just shows you don't understand what infinity is, and that you are too stupid to understand your stupidity.
There is no rule of logic that actully says that because no finite set of items reaches 1% of another that the full infinite set of them won't.
This just shows that you are the poster child for Dunning-Kruger.
You don't seem to understand what "potential" infinity actually means, or even the definition of a "set", as the set of FISONs *IS* a fixed quantity, not something that changes. We my "discover" more elements as we run the generative method, but they were always there.
I guess in your mind "truth" just isn't an established fact, but changes depending on where and how you look, so you "logic" just blows itself, and you ability to think, to smithereens on the inconsistancies you generate.