>>11509452Infinity is not a number though. It isn't used to describe a "set-in-stone" amount the same way you'd say there are 10 apples, 7,000,000,000 people, or 365 days in a year.
10; 7,000,000,000; 365; these are all numbers used to describe amounts.
Infinity isn't a number though, so it can't be used the same way.
Infinity isn't "set-in-stone" like 10 is.
10 apples, 10 people, 10 days; regardless of what is being counted, if there are 10 countable elements, then you'll have 10, distinct from 9 or 11.
refer to
>>11508995 where the size of the set A is noted. Infinite size here is not some extension of the numberline, but rather it encompasses the numberline. "1", "2", or "10" are all elements within infinity, and not merely in the sense that "1, 2, and 10 are all elements of 13" as if they're implicitly being added together. The never ending possibilities of increasingly large integers greater than 0 are what define infinity.
To say "0.999..." has "infinity 9's" is to say it simultaneously has all consecutive finite counted elements listed within the "infinite" set. But given there is no indication of how all these elements are being simultaneously invoked, be they adding/multiplying/factorializing/etc, (aka 1+2+3+... / 1×2×3×... / etc), then theres no honest sensible approach, and given trying to define "all" elements of something that never-ends, it's even less intelligible. "All" elements of a set with 10 elements is 10. "All" elements of a set with unlimited elements is... not a knowable number.
