Furanku wrote:I really resent these problems.
If we look at the ratio of balls left in to balls taken out, every interaction, we get (10 balls in - the ball out)/(the ball out).
For n interactions, this is 9n/n.
Obviously, resolving this to n=infinity, we get 9(infinity/infinity), which cancels to 9(1/1), or 9.
So even after an infinite number of interactions, we still have a ratio of nine balls in to 1 taken out.
It just doesnt seem right to me to resolve this type of question with a "lul but i is subtracting infinity from infinity wich is 0 so there be nun" equivalent.
Lets say that we take out the lowest number ball at each interaction. Interaction 1, removed ball = 1, highest ball = 10. Interaction 10, removed ball = 10, highest ball = 100. For any arbitrarily large number of interactions, the number of balls remaining = 10n-n = 9n, lowest ball remaining: n+1, highest ball remaining = 10n. Suddenly claiming that there are 'no' balls remaining after an 'infinite' number of interactions may be mathematically possible, but since mathematics tends to have problems with the concept of infinity (or atleast in the methods you're using), not necessarily logically so.
As for what numbers are on the balls removed, it seems like an illogical question for a jar theoretically containing 'infinity' balls.
Of course, I'm obviously wrong with all of this and am going to be crucified because I didn't say 'probability', or show any understanding of statistics.
No crucification. I thoroughly agree, especially with the part where you use bad grammar to convey your utter contempt for the preposterous claims of infinity-infinity = zero. And, you saved me a whole lot of typing, since you already said most of what I was going to say.
(What he said!)
I'll also add, though, that it's preposterous to keep on using "math" with a symbol in it that's undefined. Or to put it another way, to use operations on a number that they cannot be applied to. Infinity is undefined...just like ZERO. (Zero is defined, rather, but it's almost never specified. It's a useful fiction, but particularly when you're dealing in physics, you better be damn sure you know zero of WHAT, zero WHERE and zero WHEN. "A zero of apples on that table right now" does not equal "zero universes" and never will. So, like I said, unspecified. )
Edit: Sorry for the bump, didn't notice the date on the thread.