[afiori]

Often in math the property (a + b) * c = ac + bc is more useful than the repeated addition[0]

So if you try to find the zeroth operation in this fashion you get (a ? b) * c = ac ? bc which is satisfied[1] by a ? b = max(a,b) or a ? b = min(a,b).

[0] (a + 1) * c = a*c + c

[1] I do not remember whether these are the only two solutions but with min you get tropical geometry[2]

[2] https://en.wikipedia.org/wiki/Tropical_geometry