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After attempting to digest everything discusses, although realizing your desire to not require any corresponding impact to either rsrx or exact semantics; I don't believe it's reasonably possible, as it seems that the only way to achieve what you desire, and maintain reasonable consistency with mixed exact/inexact arithmetic would be to: - as suggested by "bear", define the requirement that exact and inexact value representations be constrained to the same value range. - define infinites and their reciprocals to abstractly commonly represent the greatest/smallest values at bounds of the representable numerical range, exclusive of 0 representing an absolute 0, who's reciprocal is itself 0. - thereby the range of all numerical transforms map to a correspondingly representable domain (although may optionally signal a run-time exception as may be desired in certain circumstances). Which overall seems to eliminate all the contentious issues, as long as one is willing to accept the consequences saturating arithmetic, in lieu of an typically arguably less useful more abstract treatment of infinites. Effectively resulting in: .. -1.0 .. | .. +1.0 .. -1/0 .. -1/1 .. -0/1 | +0/1 .. +1/1 .. +1/0 -------------------- 0 --------------------- (multiplicative inverse axis) -0/1 .. -1/1 .. -1/0 | +1/0 .. +1/1 .. +0/1 .. -1.0 .. | .. +1.0 .. | (additive inverse axis)