I am trying to prove that the language L = {a^n! | n>=0} is not context free using pumping lemma. But i am stuck at how to divide into uvxyz itself. Since its only one symol i find it very tricky.
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Look at the language P that results from pumping a given word w from L. There is w itself and infinitely many longer words all in a distance of |vy| from the next one, because every pumping adds |vy| symbols.
On the other hand the gap between two factorials gets all the time bigger. Obviously, for example (|vy|+2)! - (|vy|+1)! > |vy|. But this means that there is some word in P between a^(|vy|+1)! and a^(|vy|+2)!. as this word is not in L, the pumping condition is violated.
