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*To*: Per Bothner <per@xxxxxxxxxxx>*Subject*: Re: infinities reformulated*From*: Alex Shinn <alexshinn@xxxxxxxxx>*Date*: Tue, 31 May 2005 14:21:50 +0900*Cc*: Chongkai Zhu <mathematica@xxxxxxxxx>, srfi-70 <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*Domainkey-signature*: a=rsa-sha1; q=dns; c=nofws; s=beta; d=gmail.com; h=received:message-id:date:from:reply-to:to:subject:cc:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=Otfh4ZW7SzGqR93VWm1vBVo0wRvt2gvCN7mkAK3IvhcanveoyLxTg3IOCKkHnMpsxgZkS+ukwGrGmeUlWRGCWNMsUmp/a+Sx7CiEETqb9gRbI9uFkfMYq9O87fakryVCZ1qTNxo74iuDkDucNKjYgEe8gZEu+ntVVMGin0smI6g=*In-reply-to*: <429BE2BD.9080104@xxxxxxxxxxx>*References*: <20050531013438.308C813AD@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <5fb7e08705053018594e807371@xxxxxxxxxxxxxx> <429BE2BD.9080104@xxxxxxxxxxx>*Reply-to*: Alex Shinn <alexshinn@xxxxxxxxx>

On 5/31/05, Per Bothner <per@xxxxxxxxxxx> wrote: > Alex Shinn wrote: > > > > 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. Chongkai was talking about the BigFloat implementations in MacLisp and Perl. Floating point representations are limited. And the SRFI is specifically talking about inexact infinities. Symbolic manipluation systems can implement irrationals and transcendentals in many ways, but these are not inexact numbers. The very concept of inexact implies you're using a limited representation which loses information. But for the sake of argument, even exact numbers are limited on a finite computer architecture. We like to pretend bignums are unbounded, but they aren't. BigRationals have the further problem that even if the computation itself isn't getting any larger, repeated arithmatic can cause the representation to require more and more memory. More complete symbolic representation systems such as algebraic roots or Taylor series can become exponentially larger in simple repeated calculations when even fewer terms are able to cancel out. Unless you have the good fortune to be using a Turing machine everything is limited. -- Alex

**Follow-Ups**:**Re: infinities reformulated***From:*Per Bothner

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

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

**Re: infinities reformulated***From:*Per Bothner

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