How could we prove the following modified Pumping Lemma:Let the language L has an infinite number of words, then there are words $x,y,z \epsilon \Sigma ^{*}$, so that $|xz|\leq |\Sigma_{k}|$, and each word $xy^{(i)}z, i\geq0 $ is in L.Could you give me a hint how to begin?
Modified Pumping Lemma
regular languages