I'm in a proofs class and we were discussing induction. One of the most common ways we (the students) had seen induction was to represent "Statement P hold for $n$" by $P(n)$. Thus, we take the inductive hypothesis of assuming $P(n)$ is true and turning attention to $P(n+1)$. Of this format, my professor said "It's not really the best style and we won't use it that often".
Why would he say that? I've only ever (previously) seen induction in that format and he didn't really explain what he meant.