Doesn't even have to be arbitrary length.
replyWhenever you map into a smaller space, you get collisions. The bigger space doesn't have to be infinite.
with a password you may be mapping into a smaller space or a bigger space, because what you want is to get them all same length, but yeah you may in some cases be mapping into a smaller space, hadn't thought of that, although I sort of also think it is unlikely.
replyBut there it doesn't matter anyway because the password is put together with the email to identify the user so in practicality passwords will never collide even if they could in theory.
For passwords: the input _space_ is bigger. That doesn't say anything about the length of any particular password.
reply> But there it doesn't matter anyway because the password is put together with the email to identify the user so in practicality passwords will never collide even if they could in theory.
For passowrds, you are not worried so much about two users accidentally getting the same hash, you are worried about people finding a pre-image that hashes to the same output as your user's password.