Yeah, I agree the author is abstracting so much that the object he's defining doesn't have any useful property left. I genuinely smiled when the article says "

Yeah, I agree the author is abstracting so much that the object he's defining doesn't have any useful property left. I genuinely smiled when the article says "any function". "Any function" in math means any function :-) There's a reason why theorems involving arbitrary functions start with a list of qualifiers as hypotheses.