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*To*: alexshinn@xxxxxxxxx*Subject*: Re: infinities reformulated*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Tue, 31 May 2005 12:45:13 -0400 (EDT)*Cc*: mathematica@xxxxxxxxx, srfi-70@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <5fb7e08705053018594e807371@xxxxxxxxxxxxxx> (message from Alex Shinn on Tue, 31 May 2005 10:59:56 +0900)*References*: <20050531013438.308C813AD@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> <5fb7e08705053018594e807371@xxxxxxxxxxxxxx>

| Date: Tue, 31 May 2005 10:59:56 +0900 | From: Alex Shinn <alexshinn@xxxxxxxxx> | | 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 | - that is the definition of irrational ... | | But your original statement was "arbitrarily big," not "unlimited," | and this should be allowed. Infinity in this case could be defined | as the range of all real numbers greater than the largest possible | BigFloat using all of memory for the exponent. Very clever! You have rescued the "6.2.2x Inexactness" section (from bigfloats).

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

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

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