User blog comment:TechKon/Left-right arrow notation/@comment-5150073-20150810092730/@comment-5150073-20150811124215

I think a↔b = ((a-1)↔b)↔(b-1)  is wrong because a  ↔ b is supposed to be a^^^...^^^a with some number of ^'s, but  ((a-1)↔b)↔(b-1) is already   ((a-1)↔b)^^^...^^^ ((a-1)↔b)  with some number of ^'s.