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

On 11/16/2024 2:22 PM, Moebius wrote:

Am 16.11.2024 um 23:16 schrieb Chris M. Thomasson:

On 11/16/2024 2:11 PM, Moebius wrote:

Am 16.11.2024 um 22:48 schrieb Chris M. Thomasson:

On 11/16/2024 1:29 PM, FromTheRafters wrote:

Chris M. Thomasson pretended:

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(infinity - infinity) = undefined
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?

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https://en.wikipedia.org/wiki/ L%27H%C3%B4pital%27s_rule#Other_indeterminate_forms

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Or this one: https://en.wikipedia.org/wiki/Indeterminate_form
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"oo - oo" is an "indeterminate form".
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I must be missing something: [...]
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[1] = a gallon of water out of an infinite pool
[2] = another gallon of water out of an infinite pool
[3] = on and on... taken to infinity...
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The pool would always have infinite water for this process?

 Assume that the H2O molecules in the pool are "numerated" by 1, 2, 3, ... (i.e. that ALL H2O molecules in the pool are "numerated" by natural numbers).
 Taking out the "infinite amount of H2O molecules" numerated by 1, 2, 3, ... would lead to an EMPTY pool.
 On the other hand, taking out the "infinite amount of H2O molecules" numerated by 2, 4, 6, ... would not drain the pool. 😛 It would still be filled (sort of) with infinitely many H20 molecules. 😛
 Be aware if the infinite, man!

Shit.... Humm.... For fun, what about an infinite waterfall dumping into an already infinite pool, two separate objects. The pool will always accepts more water since it is infinite. Now, taking an infinite number of gallons of water out of the pool is interesting because of the infinite waterfall?
Damn infinity! beware? ;^)