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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: My ideas about infinity in Scheme (revised)*From*: Alex Shinn <alexshinn@xxxxxxxxx>*Date*: Sun, 22 May 2005 20:46:53 +0900*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:in-reply-to:mime-version:content-type:content-transfer-encoding:content-disposition:references; b=TYO25LwQmifCfwpcPRA/Ri6OpluXhZ4MR0uzGk6DiWXBzGSV4IwsOEsDgmdgLA7T0co84IoLjyb6gULWqtW0Nxc+/wAYHKXq7TWRHVvIiIxn8yS6A1Nwtgy5fBcDU6DQCR2Jk2Dx9KMCEfQYXd6RUPFVqSm8SnuhiH9dFW/EZqU=*In-reply-to*: <20050521191440.B6AAB1B77B4@xxxxxxxxxxxxxxxx>*Reply-to*: Alex Shinn <alexshinn@xxxxxxxxx>*Resent-date*: 23 May 2005 12:57:53 -0400*Resent-from*: agj@xxxxxxxxxxxx*Resent-message-id*: <20050523165753.ACB4E1B77B4@xxxxxxxxxxxxxxxx>*Resent-to*: srfi-70@xxxxxxxxxxxxxxxxx

On 5/22/05, Aubrey Jaffer <agj@xxxxxxxxxxxx> wrote: > > | Even if this SRFI won't specify exact infinity, it should not use > | the "syntax of numerical constants" 1/0 and -1/0, but +inf.0 and > | -inf.0 instead, so that a latter SRFI can use 1/0 and -1/0 as exact > | infinity. > > In hundreds of years of using rational numbers, mathematicians have > not discovered 1/0 to be a useful extension to the rational numbers. Well, mathematically 1/0 isn't real or complex either, as it doesn't obey the properties of a field and breaks the fundamental theorem of algebra. Nonetheless it's a useful concept, particularly in limited computer mathematics, and has precedent in other languages. The lack of precedent in rational infinity is likely due to the lack of rationals in other languages. I see no particular reason why real infinity should be any more or less useful than rational infinity. However, there are efficiency concerns, and many Schemes will want to implement infinity implicitly in terms of hardware IEEE floats. This is an argument for making infinities only inexact reals, though then you'd also be implicitly moving 0/0 into the reals. > While the number syntax of R5RS can be readily extended to include > +inf.0, -inf.0 (because of the leading sign). "nan.0" runs afoul of > R5RS 2.1 Identifiers: I've seen "+nan.0" used. Personally I prefer "0/0". -- Alex

**References**:**Re: My ideas about infinity in Scheme (revised)***From:*Aubrey Jaffer

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