According to this video, EXP has problems that are exponentially difficult to check.
But according to this video, EXP are problems that are exponentially difficult to solve.
It would make sense to me, that if EXP contains problems that are exponentially difficult to check, that they would contain problems that are harder than NP-complete ones.
However, if it's true that EXP is problems that are just solvable in exponential time, why wouldn't they be equal? Wouldn't EXP therefore be a subset of NP (and so would R), as problems that are harder (like R) are still solvable in "non-deterministic" time? Because the term "non-deterministic" extends to any finite amount of time, correct?
Thank you in advance for resolving my confusion. If you could explain it as simply as possible, I would appreciate it, as I get easily bogged down by the set theory.