# Relationship between L and PSPACE

The problem is: Give a self-contained proof that $\mathsf{L} \neq \mathsf{PSPACE}$ where:
$\qquad \mathsf{L} = \{ L \mid L \text{ is a language decidable in logarithmic space} \}$ and
$\qquad \mathsf{PSPACE} = \{ L \mid L \text{ is a language decidable in polynomial space}\}$.
• Just take e.g. $f(n)=n^2$ and follow the proof of the space hierarchy theorem. – Shaull Mar 25 '13 at 6:45