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*To*: per@xxxxxxxxxxx*Subject*: Exact irrationals*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Tue, 31 May 2005 12:29:26 -0400 (EDT)*Cc*: srfi-70@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <429C09BC.5090204@xxxxxxxxxxx> (message from Per Bothner on Mon, 30 May 2005 23:52:44 -0700)*References*: <20050531013438.308C813AD@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <5fb7e08705053018594e807371@xxxxxxxxxxxxxx> <429BE2BD.9080104@xxxxxxxxxxx> <5fb7e08705053022211951ff45@xxxxxxxxxxxxxx> <429C09BC.5090204@xxxxxxxxxxx>

| Date: Mon, 30 May 2005 23:52:44 -0700 | From: Per Bothner <per@xxxxxxxxxxx> | | ... A language implementation could have exact "infinite-precision" | real arithmetic to the same extent that it has "infinite-precision" | rational arithmetic. The former is even more resource-hungry, and | has some serious limitations in that comparing two exact real | numbers isn't always possible. But it still makes sense to allow | for exact real arithmetic. Scheme having exact irrational numbers is not possible within the constraints of R5RS section 6.2.4 "Syntax of numerical constants" and section 6.2.6 "Numerical input and output": ... The procedure `number->string' takes a number and a radix and returns as a string an external representation of the given number in the given radix such that (let ((number NUMBER) (radix RADIX)) (eqv? number (string->number (number->string number radix) radix))) is true. It is an error if no possible result makes this expression true. All numbers are required to have an external representation. An exact irrational number syntax would need to be added.

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

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

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

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

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

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