This is false, unfortunately, because you can't have a "uniform" probability measure on the positive integers. Here's a proof, in french.pic.twitter.com/USKMtloF7n
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This is false, unfortunately, because you can't have a "uniform" probability measure on the positive integers. Here's a proof, in french.pic.twitter.com/USKMtloF7n
1) Could you explain/give 1 scenario where the the proof fails? I appreciate it. 2) how about a discrete uniform probability distributions? (but I guess we have infinitely many primes so wouldn’t make sense for the proof of the general case.)
A bit of pedantry: you have to be very careful with the statement "at random" because a uniform distribution over an infinite set is tricky to define. But yes.
Is it more correct to say: The limit as n -> infinity, any two integers less than n, etc.?
Define "at random" please. What distribution?
As per previous replies: treat this result as a limit of uniform distributions over the first N natural numbers.
Someone can help me, how to pass from primes to integers?pic.twitter.com/95yK1yQIG1
The reciprocal of this number is in your yearbook, if I signed it.
Yes, the reciprocal. And it all has to do with Euler products. This presentation is a bit loose but that's the idea.
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