# Confused about pumping Lemma, what am I missing?

When I apply pumping slogan in this language:
$${L = {010 ^ n: n ge0 }}$$ about the alphabet $${ Sigma = {0,1 }}$$ I understand that it is not regular despite the fact that it is regular.

1. leave $${n = 4}$$, so $$w = 010000$$
2. $$w = xyz$$ , $${ mid xy mid leq n}$$ Y $${ mid and mid geq 1}$$
3. $$x = 0$$ , $$y = 10$$ , $$z = 000$$
4. leave $$i = 2$$
5. $$xy ^ 2z = 01010000$$ $$no in L$$ so L is not regular.

So, what am I missing?