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*To*: Alex Shinn <alexshinn@xxxxxxxxx>*Subject*: Re: infinities reformulated*From*: Per Bothner <per@xxxxxxxxxxx>*Date*: Mon, 30 May 2005 21:06:21 -0700*Cc*: Chongkai Zhu <mathematica@xxxxxxxxx>, srfi-70 <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <5fb7e08705053018594e807371@xxxxxxxxxxxxxx>*References*: <20050531013438.308C813AD@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <5fb7e08705053018594e807371@xxxxxxxxxxxxxx>*User-agent*: Mozilla Thunderbird 1.0.2-1.3.2 (X11/20050324)

Alex Shinn wrote: >On 5/31/05, Chongkai Zhu <mathematica@xxxxxxxxx> wrote:

And your statement "the precision of an inexact (or exact) number representation cannot be unlimited" is wrong. For example, Mathematica implements "unlimited precision number", although it may have some flaws.It cannot be "unlimited" in the sense that it is at least memory limited. No matter how much memory you have, you can never exactly represent the square root of 2 with a floating point representation

The message you quoted did not say "floating point". There are finite ways of representing trancendentals. "The square root of 2" is one. A more interesting apprach is to use continued fractions. For example see http://portal.acm.org/citation.cfm?id=31986 (I don't remember if they use continued fractions.) -- --Per Bothner per@xxxxxxxxxxx http://per.bothner.com/

**Follow-Ups**:**Re: infinities reformulated***From:*Alex Shinn

**References**:**Re: infinities reformulated***From:*Chongkai Zhu

**Re: infinities reformulated***From:*Alex Shinn

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