Why do some people write n before m?
This might sound silly, but I never understood why some people have a predilection for writing n before m.
When it comes to any other pairs of letters, like (a,b), (f,g), (i,j), (p,q), (u,v), (x,y), they are always written in alphabetical order. Why do people make an exception for (m,n)? Here are some examples:
- Let A be an nxm matrix.
- (when defining a multiplicative function): f(n)f(m)=f(nm) for any n,m with gcd(n,m)=1
- Chinese Remainder Theorem: Z/nZ x Z/mZ is isomorphic to Z/nmZ whenever n and m are coprime.
- gcd(F_n,F_m) = F_gcd(n,m) [Fibonacci numbers]
- the wedge sum S^n ∨ S^m
As can be seen, I am not talking about situations in which n appears before m by accident, but by deliberate choice. Is there a historical reason for this? Where does this trend come from and why do people prefer writing this way?