Infinite amount of monkeys playing chess

There are number systems that allow operations on infinity.

http://en.wikipedia.org/wiki/Surreal_number

You can of course make up a system in which by definition you make up numbers and, and make up operations and define them.  You can make the system logically consistent.  The names you give the numbers and operations can be the same as the operations used in the real world.  However, this is basically circular reasoning and the results would not necessarily correspond or serve as a model for any thing that happens in the real world.  If fact, pure mathematicians delight in coming up with math systems that have no practical value or relationship with the real world. 

For that matter, 0 and negative numbers are made up and have nothing to do with the real world. Oh sure they're logically consistent but how often do you have negative one of something? Or what about that weird pi number? Do you count one, two, three... pi? No! I say we should ignore its existence and everything that relies on it should be destroyed immediately.

Or we could do better than a Dark Ages monk and use the tools that do actually work, even if they have no obvious connection to the "real world".

Oh, man, don't get me started on imaginary numbers.

It's bad enough we never have a negative number of something, but why then would we want to calculate its square root?

Oh yeah they do. My wife's checking account and a couple of her credit cards prove that to be a falsehood.

While imaginary and negative numbers don't actually exist in the real world, they have a practical use and can be used to form a mathematical model of things that do exist in the real world.   This is not necessary true of every mathematical system that you can dream up.

We aren't talking about a practical, real-world situation. We are talking about infinite chessplaying monkeys.

And all the infinite support that is required to go with that supposition.

Who cares about the Infinite Monkeys playing chess in a fake universe; and chess is just a figment of the imagination of a bunch of Dweebs. The only thing here that is real is the Dweebs.

Actually, it's fairly simple to do calculations with infinity.  

Just because it's over your head doesn't mean you need to throw a hissy fit. Breathe, relax, count to... infinity

I'm half way there.

I am at aleph 10.  It's tough going though.

So, numbers don't... count?

It is interesting that indigenous tribes in, for instance, South America and Africa, do not have words for numbers higher than two or three.

So one, two, three, lots?

I find it interesting that the concept of zero was a late addition to our numeric system.

That was the Greeks fault.  They didn't like zero one bit.

I recall that there was a small group of people in Ancient Greece who would hunt you down and murder you if you suggested that the number zero existed. Or something like that. Overall the Greeks made significant leaps from the Egyptians and Babylonians but they were still limited to what they could think of geometrically. Zero just doesn't square with that.

In Mesoamerica and India, on the other hand, the concept of zero was grasped pretty quickly.

Hmm, well. How would we get the infite amount of monkeys to play gently, sitting hours to play against each other?

If something is to be infinite, it is spawning all the time in order to prevent it from stopping to exist. If it stops to spawn more of the thing, which we call p, it will no more be infinite, but a measurable number. X is the infinite spawning, and m the amount of monkeys we end with.

So p * ?x...= m

Infinite means neverending, thus can't be measured.

Infinity IS a measure.  How many integers are there?  Infinite.

How many real numbers are there?  Also infinite, but a different, bigger infinity to the first one.

Important to distinguish between infinity in maths, and elsewhere as well.  Maths admits infinity really easily.  Science struggles with it.