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> Some new possibilities have come to light. Here are all the possible > Scheme infinity notations that I know of: > Notations C and G use a trailing `.' to indicate inexactness as K > does. This requires a small extension to R5RS number syntax, as > rational notation (`1/0') does not currently allow a trailing period. - however may not be necessary if +Inf is symbolically defined as +1/0. And I'll concede my perceived necessity to denote an ambiguously signed infinity in exchange for the prevention of incorrectly signed infinities, which means that the region about 0 must be considered correspondingly invalid, (i.e. both are considered NaN or 0/0). yielding: / NaN \ or equivalently: / 0/0 \ / | \ / | \ -Inf | +Inf -1/0 | +1/0 ------+------- (reciprocal projection axis) ------+------ -0.0 | 0.0 -0.0 | +0.0 \ | / \ | / \ NaN / \ 0/0 / | | 0 0 (negative projection axis) (negative projection axis) (where NaN and +-Inf may be thought of as symbols defined as 0/0 and +-1/0) Which helps eliminates the ordering concern, although it's likely still a good idea to define (= -0.0 0 +0.0) => #t, and (< -0.0 0 +0.0) => #t, etc. However then 0/0 denotes all ambiguities in either sign or value, even those which may be very small, then Therefore: (+ +0.0 -0.0) => 0/0 [aka NaN] as otherwise: (/ (+ +0.0 -0.0 +0.0)) :: (/ (+ 0 +0.0)) :: (/ +0.0) => +Inf [which would be incorrect] Thereby one can argue that this is actually good, as then the iterative sum of alternating infinitely small value about 0 is considered ambiguous, which would typically be the case. and correspondingly yield 0/0 for all ambiguities in either sign or significant magnitude. (tan pi/2) => 0/0 (/ 0.0 0.0) => 0/0