i. Almost every positive integer is composite.
ii. Almost every prime has more than 1000 digits.
Are the above statements true?
Please comment.
(In reply to
re: mostly a discussion by Steven Lord)
This raises an interesting mathematical question, I think: Suppose there are a countably infinite (aleph naught) number of timers set to go off at some undetermined time within the next ten minutes. After 10 minutes they will all have gone off. At what time are there a finite number still counting down as opposed to an infinite number?
If the settings were truly instantaneous (I think this is something Relativity precludes--that is any simultaneity), for ten minutes there'd by Aleph-null timers counting down, and then in an instant, all would stop at the same time, leaving none still counting down.
If the countdown time is uniformly distributed between 0 and 10 min (any of aleph-one times), are there not always an infinite number of timers counting down at _all_ times 'till the end?
I think not, as there are Aleph-One possible times (unless time itself is quantized). I think this brings in a paradox. Even with "only" Aleph-null timers you could always find another time set to go off after any given timer if you go far enough in your search, yet there indeed are only Aleph-null timers; how can they compete with the Aleph-One possible settings?
I agree it's a paradox.
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Posted by Charlie
on 2018-09-25 15:57:25 |
re(2): mostly a discussion
