@Martin saidActually as ATousand has explained "infinity " is a symbol not a number.
The barrel would contain twice the infinite number of pebbles versus the bag containing an infinite number of pebbles
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 saidNo. 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.
???
Isn't that what I just said
@Ponderable saidI think we all agree on scenario 1 ... both barrels have 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 w ...[text shortened]... st number and less so a "double" of the biggest numer (which would proove that the "biggest" wasn't.
And what is your take on scenario 2?
@Paul-Martin saidScebario 2? The second option from post one is just symmetric to the first, so odd and even numbered pebbles are reversed.
I think we all agree on scenario 1 ... both barrels have an infinite number of pebbles.
And what is your take on scenario 2?
@Ponderable saidNo it is not.
Scebario 2? The second option from post one is just symmetric to the first, so odd and even numbered pebbles are reversed.
Day 1: pebble #1 removed from barrel to bag
Day 2: pebble#2 removed from barrel to bag
et cetera.
My understanding is that the barrel is empty after an infinite amount of iterations
(Contrary to common-sense)
@Paul-Martin
I reread:
* the barrel won't eb empty since you add two pebbles ab´nd remove one.
* Of course the bag would contain the lowest numbers while the barrel yould contian the highest numbers, but as said befire if you approach infinity both halves will approach infinity.
@Ponderable saidIn the first scenario the contents of both barrel and bag are easily defined.
@Paul-Martin
I reread:
* the barrel won't eb empty since you add two pebbles ab´nd remove one.
* Of course the bag would contain the lowest numbers while the barrel yould contian the highest numbers, but as said befire if you approach infinity both halves will approach infinity.
The barrel contains the set of ALL odd numbers and the bag contains the
set of ALL even numbers. Both are infinite.
In the second scenario the contents of the bag is the set of ALL
natural numbers (N) which is obviously infinite.
So what numbers are in the barrel? How can the contents be described?