Hunchman801 wrote:First of all, the theorem states that one monkey hitting keys at random forever will almost surely type any finite string. It says nothing about an army of monkeys, infinite or not, but we'll get there.
Ah, < had always heard it as an infinite amount of monkeys.
Hunchman801 wrote:Ambidextroid wrote:That being said, the likelihood of the monkeys typing any string increases proportionally to the amount of monkeys, and if the amount of monkeys is infinite then the possibility of them writing every conceivable word is multiplied by infinity, in other words an infinitely large possibility or 100%.
You can easily see why adding an infinite numbers of monkeys won't change the probability, therefore your assertion that said probability is proportional to the number of monkeys is incorrect. Don't forget that probabilities can never exceed 1.
Whoops, < may have gotten "proportional" wrong.
Still, what I was trying to say is that adding more monkeys to a room for a set time increases the probability that they'll type any specific string. Leaving one money for an hour with a typewriter is probably not going to get you any words, but if you leave a million you're much more likely. < probably didn't mean to say proportional, < meant that as the number of monkeys approach infinity, the probability of any specific string appearing approaches one.
Hunchman801 wrote:Interestingly enough, your incorrect proof led you to the right value as the monkeys (whether one or all, whether they're finite or infinite) have a 100% chance of typing a given finite string. It means that the probability is 1, which translates as almost sure, not sure or guaranteed. No paradox here.
What < meant by paradox is that a probability of 1 would usually mean guaranteed (for example, what's the probability of flipping heads with a coin that has two heads) but at the same time as demonstrated here, a probability of 1 could mean "almost certain" with a possibility of failure.
Maybe mathematically that's not paradoxical but it seemed to < to be somewhat contradictory, that a mathematical probability of 100% could fail.
And sorry about not addressing the maths you used, < isn't familiar with the details and the notation. < has a habit of forming conclusions about things in <'s head that < hasn't learned about so as a result < articulates <'s self really poorly even to <'s self
