=+4.1. 2.11 The limits superior and inferior of a numerical sequence {x,) can be defined as the supremum and infimum of the set of limit points-that is, the set of limits of convergent subsequences. This is the same thing as defining

(4.30)

lim supx, = A V xx n=1k-n and

(4.31)

lim infx, = V Axx.

n