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: <firstname.lastname@example.org> <200404260641.CAA06324@smc.vnet.net> <email@example.com> <200404281056.GAA12294@smc.vnet.net> <firstname.lastname@example.org>
- 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