Are all physical quantities an equivalence relation?

[Happiness]

Consider this self-evident proposition: "If object A has the same mass as object B and object C separately, then object B has the same mass as object C." Why isn't this stated as a law, but the zeroth law of thermodynamics is?

Is there a physical quantity u such that the u of A is equal to the u of B and separately to the u of C, but the u of B is not equal to the u of C? (It is not right Euclidean.)

Is there a physical quantity u such that the u of A is more than the u of B, and the u of B is more than the u of C, but the u of A is not more than the u of C? (It is not transitive.)

Edit: More precisely, the topic question should be "is the relation brought about by every physical quantity an equivalence relation?", which is rather mouthful.

 

[fresh_42]

A quantity is a property or an attribute, whereas a equivalence relation is a relation between two properties. So its per se not the same thing. As soon as you measure quantities or describe qualities you normally use equations which are per definition a equivalence relation.
E.g. if you look at fusion or fission processes you see that you cannot simply add up masses.