prove that L={0^i,1^j | i>j for all i,j} is not a regular language using pumping lemma

# Question on pumping lemma

**Nirbhay**#2

Choose x = 0^{P+1}1^{p}, which is obviously in L.

Then x = u v w, |v| ≥1, |uv| ≤p, and every u v^{m}w, for any m ≥0, is in L.

Considering m = 0, we know that u w is in L.

v consists of just 0s, and contains at least one 0.

So removing v removes at least one 0, which yields a string that is not in L