Well, I think you are kind of seeing the problem. Units homeomorphic to 1 are a problem in the literature, they are a different kind of problem in a units library but it is orthogonal to the discussion, we should not be side tracked here.

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Subject: Re: [std-proposals] On the standardization of mp-units P3045R1


In practice this rigorousness is (very often) not used and can get quite difficult to fully follow through.



Should pi get a unit? It can be a 180° angle, it can be a length of an arc. It is dependent on Geometry (Euclidian). There are geometries with sum of angles in a triangle less or greater than pi. Would you express the chosen geometry as a(nother) unit?



Ideally, the library allows both: Typical daily usage of units and customized more rigorous usage.

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Well, that’s because as you maybe figuring out scientist can be very sloppy with their units.



> Also, power should be measured in `W` but moment of force in `N * m`



You mean Torque. That’s because torque is actually `N * m / rad` and because torque is homeomorphic to 1 it just disappears and becomes `N * m`.

Where you to be rigorous you shouldn’t be able to just puff it out of existence.

My library actually does this to prevent this sort of confusion.



Same thing happens in Bq, there’s are actually supposed and additional unit of something that’s homeomorphic to 1 that just gets blasted out of existence.

It’s an orthogonal problem.