Math of the gods

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

Actually as ATousand has explained "infinity " is a symbol not a number.

As Cantor so aptly taught us there are diferent sizes of infinity, the smallest being "countable infinities" and that is what you have:
You have a countable infinity of odd numbers in one barrel and a countable infinity of even numbers in the other, and there is no differnce in "number" because we talk about symbols.

The prrof is simple: tell me the highest number in any of the barrel (which will represent about the half of the tiles in it). I can give you a higher number for the other, bit this can be topped again by adding one into infinity. In fact there is no biggest number and less so a "double" of the biggest numer (which would proove that the "biggest" wasn't.

@Martin said
???

Isn't that what I just said

No. You didn't factor in the fact that the barrel has one removed from it every day so the net increase is 1, not 2.

The post that was quoted here has been removed

Scebario 2? The second option from post one is just symmetric to the first, so odd and even numbered pebbles are reversed.