What Does o(1) Mean in the Longest Increasing Subsequence Problem?

[Naumberg]

Problem:

"Let x_1, ..., x_n be i.i.d random variables uniformly on [0,1]. Let X be the length of the longest increasing subsequence of x_1, ..., x_n. Show that E[X] \ge (1-o(1))(1-e^{-1}) \sqrt{n}."

Hi forum!

Using the Erdos' lemma I can only deduce that E[X] \ge \frac{1}{2} \sqrt{n}, which is a weaker bound unfortunately.

I would appreciate any further ideas!

Thanks for your help,
Michael

 

[Stephen Tashi]

What does the notation "o(1)" mean in this context?