* Lionel Elie Mamane: > Well, I have found one. Myself. You just have to interpret the part > after the second point as the integer part of an infinitesimal: > > Let ε be an infinitesimal, that is a strictly positive number > (that is ε > 0) smaller than any strictly positive real number > (that is ∀ n ∈ ℕ, n>0 implies ε < 1/n ).
Such a number does not exist because every set of reals which has a lower bound has a real number as its infimum. (Of course, such arithmetic structures can be defined, but it's a lot more involved than that.) > Then the version number x.y.z is interpreted as: > > x.y + z * ε > > (And a.b.c.d is interpreted as a.b + c.d * ε) In this context, it does not make much sense to allow only non-negative integers for z, so your interpretation is anything but natural and as good as any other total odering.
