I have a question on the definition of limsup and liminf.

First let $\displaystyle A_k = [a_n | n \geq k} $ with $\displaystyle A_k \subset A_{k-1} \subset ... \subset A_1 $

s_n = SupA_n, l_n = Inf A_n

$\displaystyle s_1 \geq s_2 ... \geq s_n, l_1 \leq l_2 ... \leq l_n $

$\displaystyle limsup a_n = lim_{k -> \infty} Sup A $

$\displaystyle liminf a_n= lim_{k -> \infty} Inf A $

I don't understand $\displaystyle s_1 \geq s_2 ... \geq s_n, l_1 \leq l_2 ... \leq l_n $

Why is $\displaystyle l_1 \leq l_2 ... \leq l_n $