Originally posted by iamatiger so the lines intersect at infinity?
I don't think I'm saying that (to be honest, geometry is not my strength and I wouldn't know how to define properly intersections at infinity). I'm saying that cardinality relations are not "continuous" in the way you describe (i.e. the cardinality of the limit is not necessarily the limit of cardinalities). The example with natural and even numbers highlights this.
Originally posted by iamatiger Possibly the problem lies in the difference between "the same cardinality" and equality?
And the problem with the balls in the bag being zero is that infinity-infinity=infinity?
Yes, I think this is key. But note that "same cardinality" is not enough. The operations with the bags must reflect the one-to-one correspondence (i.e. for any ball we must be sure it is guaranteed to leave the bag at some point).
Originally posted by Palynka I don't think I'm saying that (to be honest, geometry is not my strength and I wouldn't know how to define properly intersections at infinity). I'm saying that cardinality relations are not "continuous" in the way you describe (i.e. the cardinality of the limit is not necessarily the limit of cardinalities). The example with natural and even numbers highlights this.
Originally posted by adam warlock But I do have to say that this apparently simple problem really is head spinner. I'll post on some reputable mathematical blogs and see what the big shots answers will be.
adds 1 and 2 ballcount= 2
adds 3 and 4 ballcount= 4
removes 1 ballcount= 3
adds 5 and 6 ballcount= 5
removes 2 ballcount= 4
adds 7 and 8 ballcount= 6
removes 3 ballcount= 5
adds 9 and 10 ballcount= 7
as you can see, the ballcount approches infinity as the number of actions go up, and the number of actions are related to the time endured. therefore as time goes on the number of balls in the bag will increase and approach infinity as infinite actions are performed
Originally posted by Klasker adds 1 and 2 ballcount= 2
adds 3 and 4 ballcount= 4
removes 1 ballcount= 3
adds 5 and 6 ballcount= 5
removes 2 ballcount= 4
adds 7 and 8 ballcount= 6
removes 3 ballcount= 5
adds 9 and 10 ballcount= 7
as you can see, the ballcount approches infinity as the number of actions go up, and the number of actions are related to the time endured. therefore ...[text shortened]... number of balls in the bag will increase and approach infinity as infinite actions are performed
Originally posted by Palynka Wow, Klasker can count!
But can he read (the thread)?
Klaster is right.
Additionally, because the sets of added balls and removed balls are provably the same order of infinity infinity, and infinity-infinity = infinity (if they are the same order, and one is growing twice as fast as the other), there are an infinite balls in the bag.
Additionally, because the sets of added balls and removed balls are provably the same order of infinity infinity, and infinity-infinity = infinity (if they are the same order, and one is growing twice as fast as the other), there are an infinite balls in the bag.
Infinity is the only answer that leads to a contradiction. You can either chose "None" or "Supertasks are impossible so there is no defined answer". "Infinity" is, however, wrong.
Nice link. No idea why it's relevant, though. At no point is an operation "infinity-infinity" needed.
25 Oct '10 10:101 edit
A lot of balls
Back to Top