Sorry new to abstract algebra so if this is wrong please correct for the second example (i composite f)(a) =i(f(a)) since i is acting on the image of f(a) which is in the set B wouldn't i also have to from the set B -> B?
Your use of the word boring is annoying. First, it’s not boring to people who are struggling with the subject. Second, it’s a pretty judgmental attitude to have. Third, many great mathematicians, like Jon Von Neumann, found these functions to be the most fascinating.
Oh get a grip Andrew. He was simply making a joke about it so that the learner may have a way to remember what the identity function is going forward. Choose to dispel it as you will. Not to mention you are harping upon a creator who hasn't been active in 6 years. Math types can be quite something LOL.
