I am trying to formulate an inductive definition of string concatenation and am having a little trouble. What I've gotten so far is something like this:
(Basis) if y = empty string, then xy = x
(Step) We know a string can be build by adding one symbol at a time to the empty string, so string concatenation can take place if y = ab where a is a string and b is a single symbol (xa)b = xy
I'm having trouble with the concept, so if anyone could help me clean this up and gain a better understanding, it would really help. Thank you.