I don't know what the rigorous definition of a real number is nor even what the rigorous definition of French (texts) is but I'm pretty sure it would possible to define "reals" in terms of "French texts" in such a way that all the results hold.
Funnily enough: 0,1,2,3,4,5,6,7,8,9 are French words along with . and ,
Funnily enough: 0,1,2,3,4,5,6,7,8,9 are French words along with . and ,
So, how do we proceed to define reals in French?