Probability in an infinite sample space - sci.math

Message from discussion Probability in an infinite sample space

Han de Bruijn

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More options Mar 28 2006, 1:47 pm

Newsgroups: sci.math

From: Han de Bruijn <Han.deBru...@DTO.TUDelft.NL>

Date: Tue, 28 Mar 2006 13:47:39 +0200

Local: Tues, Mar 28 2006 1:47 pm

Subject: Re: Probability in an infinite sample space

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Dik T. Winter wrote:
> A question. For what "n" is "1/n" considered to be an infinitesimal
> quantity? That is, what is your definition of "infinitesimal quantity"?

In article

http://groups.google.nl/group/sci.math/msg/3a9c874c21c3362a?hl=en&

Robert Low wrote:
> 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.

I still feel rather uncomfortable with this comment. Because there is
some truth in it. By this I mean the way infinitesimals are _actually_
done in i.e. physics. I have an example of this and would be glad if
someone feels like scrutinizing it. It's in the following document:

http://hdebruijn.soo.dto.tudelft.nl/jaar2006/RobertLow.PDF

The problem is in the assumption at the bottom of page 1, where it is
assumed that two angles are 90 degrees, _before_ the limit is taken,
while this can be motivated only _after_ the limit has been taken.

It seems weird, but I don't know how to arrive at the result in another
manner. I would be thankful if somebody points me out how to accomplish
the same, but without being "sloppy" in this way.

Han de Bruijn

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