§ $L^\infty$ is HUGE

• Key insight: if we take any space like $L^1$ or $L^2$ or something, the terms need to eventually vanish.
• This is a small subspace $c_0$ of $L^\infty$, which is the subspace of sequences that eventually vanish.

§ Continuous functions are dense in $L^1$

§ Continuous functions are dense in $L^2$

§ Continuous functions is NOT dense in $L^\infty$