Infinite amount of monkeys playing chess

Another thing to consider is that, to produce a game, we must have two chessplaying monkeys paired with each other. You could have half of the infinite monkeys playing legally but none of the pairs produce a legal game. With a small portion of the monkeys playing chess, it is very likely that most will be assigned to a non-chessplaying monkey.

Then again, this assumes that a monkey is either going to play chess or it isn't, which is probably an oversimplification. There could be a pair of monkeys which legally move a piece in turn although they do lots of other stuff not on the chessboard in the meantime. You could also increase the number of games by considering only legal moves, so if a monkey moves the e pawn to c6 and then to e4, the c6 move would be ignored and the e4 move recorded.

But a limit is most certainly not finite. The entire purpose behind the concept of limits is to allow us to approximate that which cannot be exactly calculated, e.g., infinity.

Gabriel's horn is just a different type of infinity in that the volume portion deals with a converging infinite limit instead of a diverging (like the surface area).

It is not rational to talk of "half of the infinite monkeys" or "increasing a portion of the infinite games." In fact, you cannot rationally perform any mathematical operation on infinity (such as dividing it or multiplying it). It is not a rational number--it is merely a theoretical concept.

echecs: mind your own monkey business.

Teary: It sounds as if you are dismissing limits, and therefore all of calculus, because it is an approximation and because you seem to assume that anything involving infinity must be infinite. A limit is certainly an approximation, but the important thing is that it is as precise as we want it to be. However close you want to get, you can get there. And a limit most certainly can evaluate to a finite number though it assesses an infinite quantity.

EDIT in response to second post: by "half of infinity" I mean you could have an infinite number of nonchessplaying monkeys paired with an infinite number of chessplaying monkeys, if you prefer that to "infinity divided by two". Again, your hang-up seems to be that you want to deal with infinity as a precise, rational number, and it isn't so you throw your hands up and say it is impossible to do anything with it, we shouldn't even think about it. If you don't want to push your mind a little bit, that's fine, but some people are interested in mental exercises.

Have you even considered how mentally distressed these monkeys are with all this theory heaped on them. I sure they would have been as happy as hell to just gnaw the head off the King and not play for eternity.

Naturally, we are talking about those monkeys which channel their stress and mental instability into chess.

Are you sure we are talking about monkeys?

In calculus terms, the infinity sign is used simply to denote an unbounded limit; however, I was not talking about symbols used to represent unbounded limits. Rather, I was referring to arithmetic operations that try to treat infinity as a number, which are absurd. They are very different things.

Furthermore, there is no such thing as a perfectly precise calculation of a limit--that violates the entire concept of the term. A limit is a value which a function trends towards until it is infinitely close, but never quite reaches, hence the infinity part, i.e., the function gets infinitesimally close. You can arbitrarily just 'give up' and pick a practical number yes, but that doesn't take away the infinity part of it.

Oh...and...since we have already agreed on getting infinite monkeys, can we also throw in infinite bananas as well? I do love me some infinite banana pudding :D~

What the hell, the poor monkeys are going to start throwing chess pieces at each other because they didn't realize that life's chess answers were resting solely on the results of their games into infinity. Unfortunately nobody here is going to witness the exciting outcome.

Also, would forcing an infinite ammount of monkeys to play chess result in an infinite ammount of protests by an infinite ammount of PETA members? *shudders* :S

How come vegetation gets no respect?  They are living creatures that we kill mercilessly for food and other items.  PETA doesn't care about them?   I am 100% vegan raw organic 70% of the time so maybe I need to look in the mirror before judging PETA. 

But really, all I know about them is from that South Park episode and the Maddox article where he criticized them for not speaking out on the thousands/millions of rodents that get slaughtered by reapers every year. 

I guess if you slaughter enough of them over millions of years, they will eventually be splattered into the shape of the immortal game, move-by-move.

I don't know what you're talking about:

http://www.facebook.com/pages/PETV-People-for-the-Ethical-Treatment-of-Vegetables/354466449279

If the plants could make cute faces, they would get activists defending them.

I do like banana pudding.

Haha, what a nice idea.

So does that also mean that an infinite ammount of monkeys will eventually recreate the entire perfect game on the ground simply by flinging an infinite amount of poo around? 

An infinate number of monkeys given an infinate amount of time could create an infinate amount of things.

I estimate it would take 10,000,000 monkeys roughly 10,000 years to create the immortal game in chess.

However it would probably take 100,000,000,000,000 monkeys 1,000,000 years to creat a light saber

(Don't tell the monkeys)

Wouldn't PETV be offended that they are be called the same as PETA?   PETA folks eat vegetation from what I recall.  Or do they?   Educate me.  You can't claim to treat me ethically if you are going to bite my head off and expel my undigested parts from uranus. 

I wonder, Teary, do you also object to the use of pi?

Vegetation is at the the bottom of the food chain so nobody really gives a shit if they live or get devoured. And if they scream nobody hears it.