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*To*: MOON @ SCRC-TENEX*Subject*: Rational and complex numbers*From*: Richard E. Zippel <RZ @ MIT-MC>*Date*: Mon, 13 Jun 1983 01:22:00 -0000*Cc*: common-lisp @ SU-AI*In-reply-to*: Msg of 12 Jun 1983 19:54-EDT from MOON at SCRC-TENEX

Date: Sunday, 12 June 1983 19:54-EDT From: MOON at SCRC-TENEX To: Richard E. Zippel <RZ> cc: common-lisp at SU-AI Re: Rational and complex numbers Is there really more than one reasonable injection of Z into Q? Any map that sends 1 to an element of Q (other than 0) and all the elements accordingly is reasonable. Basically, any time you are counting things by halves, thirds, fourths or some other fraction you are presuming a different injection. (otherwise known as scaling) It might be nice to be able to have integers with these scaling factors built in. (multiples of pi or pi/4 might be nice for trig calculations. Certainly radians would be a more palatable measure of angles if the scaling factor of pi were built in. acos(0) would be 1/2(radians). When converted to floating point (the reals) it would of course give 1.57 ...) Why should these conversions be any different from the standard one? (The answer is: because it is more common) I'm not suggesting that the natural coercion from Z to Q be thrown away as much as suggesting that there is a lot more power and flexibility lurking thee than w currently acknowledge.

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