Pumping Lemma for regular language: Can we modify the first condition to 'for each i > 0'?

Question

Pumping lemma from < Introduction_to_the_Theory_of_Computation >"

Question: Can we modify the first condition to for each i > 0 instead of for each i ≥ 0 ?

Answer 1

Yes, you can do this.however it make the pumping lemma less useful. We use pumping lemma to tell a grammar is not regular and it doesn't even necessarily work for all non-regular languages Restricting its applicability a little further is fine but unnecessary, especially since the method of proof implies that you can pump the substring down as well as up.