I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books (here let's say the bible).
I believe this experience can be reduced to choosing a random sequence among real numbers:, strictly speaking the monkey could type a sequence looking like 1/3. (Characters replaced by numbers), my friend told that it is not possible, but for me this is what pure randomness is.
I also believe that not all infinite sequences contain the bible, so it doesn't make any sense to say that the monkey will almost surely write it.
My friend is sure that the monkey will ALWAYS write everything possible, while for me this implies to always choose a "disjunctive sequence".
I understand that from a probabilistic point of view, the chance that the monkey doesn't write a particular sequence drop to 0 as the number of character increase. But probability is also the ratio of specific events on all the events, since all the sequences are not disjunctive sequence, this probability cannot be equal to 1.
Who is right here?
