Is this language countable : $L= \{ w : w \in (1 + 0)^{*} \}$

Question

This is my take :

Epsilon ---> 1

0 --> 2

01 ---> 3

10 ---> 4

11 ---> 5

001 ---> 6

010 ---> 7

. . .

So therefore we can count them.

But based on this video : https://www.youtube.com/watch?v=oe-ZAJQz9Cc&index=5&list=PLsFENPUZBqiqbnD-WatYxUhRWLMNDoMun

They should not be countable, but i did not understand that video, the guy says all possible languages over $\{0,1\}^{*}$ are uncountable!