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Originally posted by iamatigerI 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.
so the lines intersect at infinity?
Originally posted by iamatigerYes, 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).
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?
Originally posted by PalynkaI think parallel 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.
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 KlaskerWow, Klasker can count!
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
But can he read (the thread)?
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Originally posted by PalynkaKlaster is right.
Wow, Klasker can count!
But can he read (the thread)?
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.
http://www.newton.dep.anl.gov/askasci/math99/math99191.htm
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Originally posted by iamatigerInfinity 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.
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.
http://www.newton.dep.anl.gov/askasci/math99/math99191.htm
Nice link. No idea why it's relevant, though. At no point is an operation "infinity-infinity" needed.