Re: Probability in an infinite sample space


Han de Bruijn wrote:
Robert Low wrote:
Han de Bruijn wrote:
Infinitesimals are just very smal real numbers. What's your problem?
Just the minor one that it doesn't work. So, let e be
an infinitesimal. (i.e. a very small real number).
But e = 1/n and that depends on n .

No, e is an infinitesimal. That's just a very small number,
remember?

Then n.e = 1 . Can't help if you
don't know how to handle limits in the way they should. Really can't
help ...

I think we can both agree that you can't help me with limits.

Sure. And all limits commute with each other. Especially if
you put your fingers in your ears and sing 'lalala' whenever
somebody tries to explain to you otherwise.
Lalala. There is no need for "commuting limits". I don't understand
where the idea comes from.

Ispe dixisti.

I'm working in a finite domain. And only
in the very last phase, when all "commuting" is over(?), let n->oo .

I thought that was my point. You're letting n tend to infinity
*after* you use your purported infinitesimal: but the infinitesimal
isn't defined until after you take the limit.

There is a perfectly well-defined
sense in which one talks about things like 'the probability
of choosing a multiple of 3', and it's asymptotic density.
I know. And that _is_ a probability. Not only "sort of".


Not by any notion of being a probability that the rest of us share.

Why not just use a tool that works instead of tying together
two lengths of baling wire and a rusty fork, and insisting
that the result is a screwdriver?
Why not being _terse_. And not define yet another framework (asymptotic
densities) if you already have one (probability theory) that should fit
the bill, just fine.

Hey, *you* are the one trying to define a new framework (infinitesimal
probabilities). The rest of us are quite happy to observe that standard
probability doesn't work here, and use a viable alternative.

.

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