These Mathematicians are very selective about which aspects of the universe they want to regard and which aspects they want ignore. Like, yeah you can take an imaginary situation and imagine that it's possible, or impossible. It can go any way because it's imaginary. No need to waste time on math, you can just imagine any outcome you like.

In reality, however, I think if you had a system that feeds a monkey a treat every time it strikes a letter key that corresponds to the next letter in a Shakespere play displayed on a monitor, you would eventually have some Shakespeare typed out by a monkey.

One could also just have a monkey mash keys for a while, and then after removing all the unnecessary letters you'd be left with a Shakespearian play.

Or, with a group of monkeys and plenty of time one could use natural selection to evolve them into a literate species that could handle the task easily. This is the method currently in use for the typing of Shakespeare. It has already been done, many times over.