If an infinite number of monkeys sat down and played an infinite number of games, could they take an infinite number of different storylines?

Of course then are the more important questions like:
Would you have to have an infinite number of monkey feeders to feed the infinite number of monkeys and would they care about playing games with an infinite number of different storylines?

If an infinite number of monkeys had to play an infinite number of games would they really have the "full freedom to do whatever" and if they did wouldn't they stop playing games and go out on a date?

If the infinite number of monkeys were always playing an infinite number of games, how would they be able to procreate and wouldn't that lead the the demise of the infinite number of monkeys making the whole study useless?

Brought to you by Monkeys for Infinite Games (MIG)