Where are all the assumptions Obviously this only holds true if  The monkey lives for ever  As t infty the support of the any probability distribution function does not decrease   The length of time the type writer is broken is not above some limit The first point is obvious The second just means that say your a monkey and you you start pressing the buttons sooner or later youd expect the monkey to realize that the biggest event happens when you press the return carriage key and thus it is entirely plausible that the monkey would never press any of the other keys again In fact there are even similar reasons this could fail It could well be the case that the width of the finger of the monkey are such that it never hits only one key rather it hits two or more which in turn could cause this theorem to fail The last point is about what if the type writer broke surely the time between break downs would have to be strictly less that than the time necessary to type the number of characters in the text