__Another One__Last Sunday, one of our colleagues presented a nice division by zero in the very applied probabilities domain.

Biasing the very clear presentation, that definitively deserves an accessible to students published note, I will say that was about the :

**dF/dG**division where, par Newton!,

**dF** and

**dG** are infinitesimally small quantities.

Par l'Hôspital!

**dF/dG** makes sense and

**dF/dG = F'/G'**, even when

**F** and

**G** are probabilities.

In practice, to apply l'Hôspital's rule to zero-probability events requires

- A missing definition (that is equivalent to introducing infinitesimal

**dP** probabilities)

- A postulate that the definition fits to the real insurance world as well as the Topology and the Theory of Measure, and

- A double column paper comparing the

**dF** calculus to the

**delta-epsilon** calculus.

By the way, here is a less known construction of the real numbers,

Definition: A real number is an equivalence class of slopes.where a slope is a map L : Z -> Z, with the property that the set {L(m + n) − L(m) − L(n) | m, n in Z} is finite.