- Michael MLv 71 decade agoFavorite Answer
In mathematics, "theory" means a coherent , systematic body of knowledge that is developed axiomatically. It does not mean "hypothesis". The word does not imply anything tentative. The word is related to the word "theorem"
So with permutations, you begin with the definition of a permutation, some other definitions like even and odd permutations, and then you prove theorems based on those definitions, introduce some new definitions (like binomial coefficients perhaps), prove more theorems based on the previous theorems and definitions, and keep going.
It is that systematic theorem-proving that makes it a theory.