Is the given proof of the following correct?
Let $\{A_n\}$ be a sequence of sets, then: $$\liminf_{n\to\infty}=\bigcup_{i=1}^\infty\bigcap_{j=i}^\infty A_j=\{\text{elements that belong to all but finitely many } A_i's\}$$
Pf.
($\leftarrow$) Let $$B_i=\bigcap_{j=i}^\infty A_j$$
Then, $$x\i...
Trying to play with symbols. If $T=\{T_i\}$ is the set of running times of every possible algorithm that solves a given problem $P$. Can we say that an algorithm $j$ is optimal if $T_j=\sup T$?
Is the given proof of the following correct?
Let $\{A_n\}$ be a sequence of sets, then: $$\liminf_{n\to\infty}=\bigcup_{i=1}^\infty\bigcap_{j=i}^\infty A_j=\{\text{elements that belong to all but finitely many } A_i's\}$$
Pf.
($\leftarrow$) Let $$B_i=\bigcap_{j=i}^\infty A_j$$
Then, $$x\i...
Computer Science
Computer Science