Math of the gods

Once upon a time, well let's just say a long time ago, there was a beautiful
mathematician, her name was Abacus. Now Zeus fancied the pants of Abacus
and as was his M.O. he transformed himself into a math nerd and impregnated
the lovely Abacus.

Abacus had a son, Cantor, who was a demi-god. He was also a mathematician
and soon he was giving away math secrets to mortal men.

The gods did not like this and Hera in particular didn't like Cantor so she exiled
him to a deserted island for eternity. She also gave him a task.

Each morning he was to take two pebbles from the beach, inscribe consecutive
numbers on them and place them in a barrel. (An infinitely BIG BARREL). So on
the first morning he inscribed 1 and 2 on two pebbles, on the second morning
he inscribed 3 and 4 on the pebbles and so on. (Forever)

Now there are two versions of this story as to what he had to do in the afternoon.

Version One: Each afternoon he had to take out the pebble with the
highest number and place it in a bag.

Version Two: Each afternoon he had to take out the pebble with the
lowest number and place it in a bag.

After an eternity of this when an infinite number of days had passed it was the
end of time and Hera looked inside the barrel and the bag. What did she find?

@Paul-Martin said
Once upon a time, well let's just say a long time ago, there was a beautiful
mathematician, her name was Abacus. Now Zeus fancied the pants of Abacus
and as was his M.O. he transformed himself into a math nerd and impregnated
the lovely Abacus.

Abacus had a son, Cantor, who was a demi-god. He was also a mathematician
and soon he was giving away math secrets to ...[text shortened]... ad passed it was the
end of time and Hera looked inside the barrel and the bag. What did she find?

@Ponderable
How many pebbles in the bags in each scenario?

@Paul-Martin said
@Ponderable
How many pebbles in the bags in each scenario?

@AThousandYoung said
Infinite 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.

@Paul-Martin said
How many in EACH bag for each scenario?

@AThousandYoung said
#stones = #day +1 /#day - 1 in the morning, #day in both in evening

@Paul-Martin said
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.

@AThousandYoung said
There is no situation where the barrel is empty once this project has begun.

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 ...[text shortened]... from infinity but you can't do that. You need to use calculus limits and there are rules for that.

The barrel would contain twice the infinite number of pebbles versus the bag containing an infinite number of pebbles

@Paul-Martin said
In scenario 2, what numbered pebbles would be left in the barrel?

@Martin said
The barrel would contain twice the infinite number of pebbles versus the bag containing an infinite number of pebbles

@AThousandYoung said
No because one is taken from the barrel each evening. Both would be equal infinities.

@Martin said
NO

TWO pebbles in the barrel in the morning and ONE out into the bag in the afternoon

@AThousandYoung said
The one that goes in the bag comes out of the 2 put in the barrel.