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

On 12/17/24 4:57 PM, WM wrote:

On 17.12.2024 18:07, joes wrote:

Am Tue, 17 Dec 2024 10:13:48 +0100 schrieb WM:

 

Every element is the last element of a FISON [1, n]. ℕ is the set of all
FISONs.

No, it is the union.

 It is also the set because every FISON can represent one natnumber.

But you don't use them that way, so you don't seem to have that property.
While 3 can be defined as the set {0, 1, 2}, which expands to
{ {}. {{}}. { {}. {{}} } }
When we talk of it as the natural number, it isn't just that set,

>

I use all FISONs.

No, you don’t. N is not a FISON.

 It is all FISONs.

No, it is a set of all Natural Numbers.

>

All intervals do it because there is no n outside of all intervals [1,
n]. My proof applies all intervals.

And all the intervals are finite, and thus not the INFINITE set N,
which is where the bijection occurs.

According to Cantor the "bijection" uses all n and nothing more.

What else do you think it uses?

 You claimed that he uses more than I do, namely all natural numbers.

Right, you never use ALL the natural numbers, only a finite subset of them.

 Regards, WM

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