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 ?
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Yes, you can do this; however, all it does is make the pumping lemma less useful for no additional benefit. The pumping lemma for regular languages already cannot tell you that a language is regular, and it doesn't even necessarily work for all non-regular languages as it is. 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. – Patrick87 May 30 '19 at 12:15
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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.
