It’s impossible for a problem to require exponential space without being exponential-time.

- Consider that if an $ EXPSPACE~~complete$ problem can be solved in $ 2^n$ time.
**It will now fall into the class $ EXPTIME$ .** - Then $ EXPSPACE~~complete$ problems are in $ EXP$
**if they can be solved in $ 2^n$ time**. This means they can reduce into $ EXP~~complete$ problems and vice versa.

To me, this should be easy to write a proof that $ EXPTIME$ = $ EXPSPACE$ .

My intuition tells me that if $ Exptime$ = $ Expspace$ ; then $ PSPACE$ != $ EXPTIME$ ,

**Because $ PSPACE$ already is not equal to $ EXPSPACE$ .**

## Question

As an amateur, what would make this reasoning be wrong or right?