Re: Incompleteness of Cantor's enumeration of the rational numbers

Am 16.11.2024 um 01:27 schrieb Moebius:

Am 15.11.2024 um 22:58 schrieb Chris M. Thomasson:
 

[...] Taking a gallon of water out of an infinite pool of water means you are holding a gallon water, but the infinite pool is still infinite. The same. Taking an infinite amount of water means the pool is still full of water.

 I already told you that this is not necessarily the case.

Assume that the H20 molecules in the pool are "numerated" by 1, 2, 3, ... (i.e. that ALL H20 molecules in the pool are "numerated" by natural numbers).
Taking out the "infinite amount of H20 molecules" numerated by 1, 2, 3, ... would lead to an EMPTY pool.
On the other hand, taking out the "infinite amount of H20 molecules" numerated by 2, 4, 6, ... would not drain the pool. :-P It would still be filled (sort of) with infinitely many H20 molecules. :-P
Be aware if the infinite, man!
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