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

On 12/30/24 3:44 AM, WM wrote:

On 30.12.2024 01:36, Richard Damon wrote:

On 12/29/24 5:31 PM, WM wrote:

 

My theorem: Every union of FISONs which stay below a certain threshold stays below that threshold.
Find a counterexample. Don't claim it but prove it. Fail.

 

But what does that prove?

 That proves the existence of dark numbers.

How?
It shows that there are numbers you didn't look at, but you admit to not looking at all the numbers.

>
The finite numbers are finite, and that is it.

 FISONs do not grow by unioning them. All FISONs and their unions stay below 1 % of ℕ.

So, all Natural Numbers are finite, but the "union" of them (putting them *ALL* into a set) creates an infinite set.

 Proof: Every FISON that is multiplied by 100 remains a FISON that can be multiplied by 100 without changing this property.
 If ℕ is an actually infinite set then it is not made by FISONs.

Who said it is made of FISONs, It could be said that it is the union of *ALL* of the infinite set of FISONs, but the union of an infinte set of things can be bigger than any member of that infinite set.

 Regards, WM
 

All you are doing is showing your utter stupidity of trying to use the logic of finite sets when you are working with an infinte set, and that logic just blows itself up into smithereens by doing so, and takes you out with it,
Your "dark numbers" are just the result of the black hole created by that explosion cause by your inconsistancies.