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

On 10.12.2024 19:18, Python wrote:

Le 09/12/2024 à 22:50, WM a écrit :

The very core property of analysis is that equal sequences have equal limits if they have limits at all.

>
E(1)∩E(2)∩...∩E(n) = E(n)
>
Lim E(1)∩E(2)∩...∩E(n) = {}
Lim E(n) = {}
>
They are equal.

>
Not in a set theory where every endsegment is infinite.

 Nonsense.

In fact some readers claim that every endsegment is infinite. Finite endsegments cannot be seen. They are dark.

 I once asked a whole classroom what they think of your claims, providing your posts/site as well as Ben's paper : http://bsb.me.uk/dd-wealth.pdf.

Ben Bacarisse's example : To keep things simple, let's number the notes 1; 2; 3; : : : and we'll give McDuck only $2 a day. One has to be returned a day.
He accuses me to confuse lim card and card lim and to use the wrong limit. But I simply need the limit of the set only with no cardinality at all. Therefore his example is mistaken. I adhere to the additional condition though that a difference between two states can consist of one note only. That makes a sequence increasing beyond all bounds with limit empty set (where all elements are claimed to have gone) impossible.
Never a student of mine has doubted that.
Regards, WM