Hash table

Is it ever possible to have a Hash table that can do get,put,remove @ O(1) for Strings?

calculating the hash for the String alone is O(n), is it not? [that's if you want to produce a good hash that won't collide all over the place]

>>108
>it's possible for a value which is defined outside of a set, to be mapped to a "true" or "false"

Are you talking about undefined behavior? Or maybe there is state that affects the output of the function that is not accounted for in the parameters, and depending on what the state is, the function application may evaluate to true or false?