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

On 12/28/24 11:50 AM, WM wrote:

On 28.12.2024 15:12, Jim Burns wrote:

On 12/27/2024 5:24 PM, Ross Finlayson wrote:

On 12/27/2024 01:00 PM, Jim Burns wrote:

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[...]

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The, "almost all", or, "almost everywhere",
does _not_ equate to "all" or "everywhere",

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Correct.
⎛ In mathematics, the term "almost all" means
⎜ "all but a negligible quantity".
⎜ More precisely, if X is a set,
⎜ "almost all elements of X" means
⎜ "all elements of X but those in
⎜ a negligible subset of X".
⎜ The meaning of "negligible" depends on
⎜ the mathematical context; for instance,

 A good example is the set of FISONs. Every FISON contains only a negligible quantity of natural numbers. A generous estimation is: Every FISON contains less than 1 % of all natural numbers. There is no FISON that contains more than 1 %. Therefore the union of all FISONs contains less than 1 % of all natural numbers. Outside of the union of FISONs are almost all natural numbers.
 Regards, WM
 Regards, WM
 

Just shows that you don't understand *AT ALL* about infinity.
Every Natural Number is less that almost all other natural numbers, so its %-tile of progress is effectively 0, but together they make up the whole infinite set.
The fact that you mind can't comprehend that just proves your stupidity.