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Message from discussion Computation using real numbers as opposed to rational approximations to real numbers
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Robert Myers  
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 More options Jan 19 2012, 11:34 pm
Newsgroups: comp.arch
From: Robert Myers <rbmyers...@gmail.com>
Date: Thu, 19 Jan 2012 23:34:34 -0500
Local: Thurs, Jan 19 2012 11:34 pm
Subject: Re: Computation using real numbers as opposed to rational approximations to real numbers
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On 1/19/2012 11:26 PM, mac wrote:

>> I just started from the interesting point that nature itself seems to be
>> discrete, not analog, down at the quantum level.

> Measurements may be discrete, but state vectors are complex continuous. And
> since they can combine via interference, I don't think it's safe to say
> Nature is discrete.

You can make many proofs go through on finite-dimensional vector spaces
and sort of wave your hands to go to an infinite-dimensional Hilbert space.

Let me say that a different way.  You can do physics on a lattice and,
at the end of the course, mention that, oh, by the way, you can extend
the methods to infinite-dimensional systems.

I know of no corresponding program for teaching real analysis.

Robert.


 
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