Sorry, but how is that a proof?

It's not clear whether there is a number A with decimal expansion (a_1 a_2 ... a_k ) such that there doesn't exist a positive number X for which

   X ! = (a_{1} a_{2} ... a_{k}  x_{k+1} x_{k+1} ... x_{s} )

for some arbitrary length s in the decimal expansion of X! .