Re: Calculus XOR Probability

Robert Low wrote:

Han de Bruijn wrote:

What !? I've resorted to the hyperreals in order to _have_ the
probability of choosing a finite integer. And that probability
turns out to be an infinitesimal in the hyperreals *R.

No, it doesn't. If N is a hyperfinite natural, and you associate
the probability 1/N with each natural 1 <= n <= N, then for any
*finite* n, the probability of choosing a natural less than
or equal to n is infinitesimal.

Yeah. And that's fine, isn't it? So we are finished. But, but, but ...

But the probability of choosing
*some* finite natural would be the sum over all finite naturals
of 1/N. Unfortunately, the finite naturals don't comprise an internal
set, and this sum does not exist as a nonstandard real.

Sorry. I don't understand even a little bit of what you are saying here.

Han de Bruijn

.

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