Re: Real numbers , what are they good for ?

On Dec 16, 2:37 pm, jane <jane1...@xxxxxxxxxx> wrote:
A bit shaky question :

A friend of mine was asked the following question:

What are real numbers good for ?

How would you answer this question, stressing properties which, differ exactly real numbers and which are useful in analysis ?

I can give my own answer as well, but i would like to see other opinions, perhaps written shorter and having more information.

Thanks.

I came across the following which may be of interest: From Alexandre
Borovik's blog
http://dialinf.wordpress.com/2007/12/17/commented-out/
referring to Vladimir Arnold's "What is Mathematics"

Vladimir Arnold forcefully stated in one of his books that it is wrong
to think about finite difference equations as approximations of
differential equations. It is the differential equation which
approximates finite difference laws of physics; it is the result of
taking an asymptotic limit at zero. Being an approximation, it is
easier to solve and study.

In support to his thesis, Arnold refers to a scene almost everyone has
seen: old tires hanging on sea piers to protect boats from bumps. If
you control a boat by measuring its speed and distance from the pier
and select the acceleration of the boat as a continuous function of
the speed and distance, you can come to the complete stop precisely at
the wall of the pier, but only after infinite time: this is an
immediate consequence of the uniqueness theorem for solutions of
differential equations. To complete the task in sensible time, you
have to allow your boat to gently bump into the pier. The asymptotic
at zero is not always an ideal solution in the real world. But it is
easier to analyze!
.

Relevant Pages

  • Re: Real numbers , what are they good for ?
    ... to think about finite difference equations as approximations of ... approximates finite difference laws of physics; ... differential equations, ... you control a boat by measuring its speed and distance from the pier ...
    (sci.math)
  • Re: Real numbers , what are they good for ?
    ... to think about finite difference equations as approximations of ... approximates finite difference laws of physics; ... differential equations, ... you control a boat by measuring its speed and distance from the pier ...
    (sci.math)
  • Explosion and fire down my pier
    ... If you didn't see the news, a boat exploded then burned five slips ... earlier by Rick and Shannon over on pier 4. ... fire hose on the dock. ... The fire and smoke was so thick, ...
    (rec.boats.cruising)
  • Re: Explosion and fire down my pier
    ... If you didn't see the news, a boat exploded then burned five slips ... earlier by Rick and Shannon over on pier 4. ... fire hose on the dock. ... The fire and smoke was so thick, ...
    (rec.boats.cruising)
  • Re: Another old photo needing identified.
    ... boat in a harbour "somewhere in England". ... It is 'The Golden Hind' next to Southend on Sea Pier. ... in the gangway being lifted away from any supporting structure if it ... merely a wooden structure sitting in a pool which gets "topped up" at ...
    (soc.genealogy.britain)
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