I think it is pointless to argue about what is the definition of a symbol. If you write your own book, you can make it whatever you want it to be. For as long as you are clear about it, it is still a good book.
W|A is clear about its interpretation.
So what is the problem then?
Also, how would you represent ratios if :
is taken for division only?
This is a bit like arguing that either Fortran, C or Mathematica is "wrong" when they denote exponentiation by **
, pow
and ^
respectively. Yet all three work just fine, and all three can compute powers.