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

Am 03.12.2024 um 06:47 schrieb Moebius:

Am 03.12.2024 um 06:34 schrieb Chris M. Thomasson:

Then the following can be shown:
       lim_(n->oo) {1, 2, 3, ..., n} = {1, 2, 3, ...} .
 

While this seems to be intuitively clear, the following is less clear (I'd say):

       lim_(n->oo) {n, n+1, n+2, ...} = {} .

:-P
That's where WM fails. For him lim_(n->oo) {n, n+1, n+2, ...} =/= {} (has to be), after all, for all n e IN: {n, n+1, n+2, ...} =/= {} [even worse: for all n e IN: {n, n+1, n+2, ...} is infinite!].

Hope this helps. :-P
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