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MathGroup Archive 2004

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Re: bug in IntegerPart ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47908] Re: bug in IntegerPart ?
  • From: ancow65 at yahoo.com (AC)
  • Date: Fri, 30 Apr 2004 19:26:48 -0400 (EDT)
  • References: <c6g015$4lk$1@smc.vnet.net> <200404260641.CAA06324@smc.vnet.net> <c6l7gv$imk$1@smc.vnet.net> <200404281056.GAA12294@smc.vnet.net> <c6qamj$s6j$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I have feeling speaking to deaf ears. Let me try again.

On one hand, there is mathematics with all these wonderful and precise
ideas. On other hand are computer programs that model (sic!) these
ideas on computer. I have impression that some of us got some much
involved with programs that forgot that they are just projections of
mathematical ideas. In mathematics 1.3 is an exact number. Decimals
can be represented on computer in number of ways. IEEE representation
is only one of many. Contrary to the belief of posters, there are
known ways to represent decimal numbers on computer EXACTLY. Just as
there are big integers, there are also big floats available in number
of languages or programs. Sorry, the charter of this group does not
allow me to list their names.  There is no apparent reason, why
Mathematica could not do the same. Additionally, there are indeed
numbers that are known only approximately and there are methods to
perform computations with such. Interval arithmetic is notably one of
such methods. As long as Mathematica's numerical model mixes these two
classes, there will side effects and confusion. I am trying to say
that the system can be improved relatively easily, the methods are
known, and the only missing factor will.  I made a constructive
suggestion. (1) Treat all decimals as exact numbers. In this way
number of problems arising on the border between Machine Precision and
Big Number Arithmetic would disappear. The mapping between decimals in
mathematics and Mathematica would become bijection. (2) Introduce a
new notation or alternatively a programming switch for inexact numbers
that would follow IEEE rules. Both developers and users will have
precision or speed as needed without compromising mathematical clarity
and precision.

AC


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