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@Paul-Martin saidInfinite because it's two per day times infinite days...if we make the assumption that Cantor is able to find a specific pebble in an infinitely large bag every afternoon.
@Ponderable
How many pebbles in the bags in each scenario?
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@Paul-Martin saidThere is no situation where the barrel is empty once this project has begun.
I'm sorry but I don't follow your shorthand.
Here is my take on it.
Scenario 1 (when highest number is removed from barrel in evening)
Barrel contains an infinite number of pebbles - all odd.
Bag contains an infinite number of pebbles - all even.
Scenario 2 (when lowest number is removed from barrel in evening)
Barrel contains no pebbles.
Bag contains an infi ...[text shortened]... umber of pebbles - all positive integers 1,2,3, ...
Seems like a paradox but I think I'm correct.
Each day the barrel gets +2 and then -1 stone. So each day there is a net increase of +1 stone. In other words, the number of stones in the barrel equals the number of days since this process began.
Infinities don't exist. But in the spirit of the puzzle you can take the limit of the number of stones in the barrel as the number of days since this started approaches infinity and you'll get infinite stones as the limit.
After first evening there is one stone in the barrel. After two evenings, there are two...after 50 evenings, there are 50....after infinite evenings, there will be infinite.
Of course we're being sloppy with our use of the word "infinity". This is a simple calculus problem involving limits approaching infinity, not actual infinities.
I suspect your difficulty is that you are trying to subtract infinity from infinity but you can't do that. You need to use calculus limits and there are rules for that.
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@Paul-Martin saidThose numbers would all be infinitely large. This doesn’t make intuitive sense because infinities don’t exist.
In scenario 2, what numbered pebbles would be left in the barrel?
After any particular evening the lowest number in the barrel will be one more than the number of the day. On day 100 the lowest number left is 101. The numbers in the barrel in Case 2 depend on what day it is. On day infinity the numbers in the barrel are infinity plus 1 through twice infinity.
@Martin saidNo because one is taken from the barrel each evening. Both would be equal infinities.
The barrel would contain twice the infinite number of pebbles versus the bag containing an infinite number of pebbles
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@AThousandYoung saidNO
No because one is taken from the barrel each evening. Both would be equal infinities.
TWO pebbles in the barrel in the morning and ONE out into the bag in the afternoon
@Martin saidThe one that goes in the bag comes out of the 2 put in the barrel.
NO
TWO pebbles in the barrel in the morning and ONE out into the bag in the afternoon
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@AThousandYoung said???
The one that goes in the bag comes out of the 2 put in the barrel.
Isn't that what I just said