HLS

Display math:

e^{i\pi} + 1 = 0

and inline math $a^2 + b^2 = c^2$.

For sequences of numbers, limit inferior and limit superior are defined as $\liminf (a_n):=\sup\{\inf\{a_k:k \ge n\}\}$ and $\limsup (a_n):=\inf\{\sup\{a_k:k \ge n\}\}$ respectively; for sequences of sets, they are defined as $\displaystyle \bigcup_{n=1}^{\infty} \bigcap_{k=n}^{\infty} A_k$ and $\displaystyle \bigcap_{n=1}^{\infty} \bigcup_{k=n}^{\infty} A_k$ respectively.