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

On 06.01.2025 13:28, Richard Damon wrote:

On 1/5/25 2:47 PM, WM wrote:

You said that I never used all FISONs. But I do. All are insufficient.

 No, you DON'T use all. Because ALL has an infinite number of members,

All are less than |ℕ|/10000.

and you need to process them one by one,

I do not process them but use my theorem: Every union of FISONs which stay below a certain threshold stays below that threshold.

but your claim doesn't match your conclusion, as the union of *ALL* the FISIONs will reach the size of the Natural Numbers, even though no finite subset reaches a measurable percentage of it.
>

How do they do it? Do one or more FISONs grow during the union process? (One would be sufficient.)

 Nope, they are just infinite in number.

The set of all rationals between 0 and 1 is also infinite in number. That is not an argument for their union to reach |ℕ|.
Regards, WM