Definition: $P$ is the set of languages that can be decided by a deterministic Turing Machine in polynomial time.
I wonder if: $P$ equals to the set of languages that can be decided by a non-deterministic Turing Machine in polynomial time?
I think this also has to be true in this case because a non-deterministic Turing Machine can also decide all problems which can be decided by a deterministic Turing Machine. Because of the fact that we have here a language in P this NTM also decides it in P.
Am I right or am I wrong?