Just something interesting if you are trying to argue with someone who have never taken a number theory class about multiplicative functions. I was talking to an engineering friend about multiplicative functions, back when we first learned that the totient function was multiplicative, and I was still really confused about multiplicativity (is that a word?). They were trying to explain it to me (really really smart person) and I basically just stopped listening because I still didn't get it or why we cared. Then I was just looking up some multiplicative functions, and found out that outside of number theory, if a function is called multiplicative, it is pretty much generally used to describe COMPLETELY multiplicative functions. And then I realized that what my engineering friend had been trying to describe to me was a completely multiplicative function, because anyone else probably has no idea of what the difference is or why it would ever matter. I don't think that I was confused because of the way they were explaining it, they had never done anything with multiplicative functions they were just using background knowledge and what they thought a multiplicative function would be. So just a warning, if you're talking to someone who has never been in number theory, they probably think that if a function is multiplicative that they can split it up however they want!

Multiplicative functions