Bring it on.
Okay, here's a nice consequence of infinity. A
are two agents who perform simultaneous supertasks. A supertask consists of a series of tasks each performed when half the remainder of a finite period of time has elapsed, in other words, an infinite number of tasks are performed in a finite time. Both A
have an infinite number of balls, sequentially labeled 1,2,3.....
and a jar of infinite capacity. A
's tasks consist of putting the ten balls with the lowest numbers, that haven't been in the jar, into the jar and removing the lowest numbered ball from the jar, so, at time one A
puts in balls 1-10
and removes ball 1
, at time two A
puts in balls 11-20
and removes ball 2
, etc. B
's tasks consist of putting the nine lowest numbered balls into the jar, but skipping all multiples of ten, and appending a zero to the number of the lowest numbered ball in the jar, so, at time one B
puts in ball 1-9
and appends a zero to ball 1
so that it reads 10
, at time two B
puts in balls 11-19
and appends a zero to ball 2
so that it reads 20
. At all times during the running of the supertask, the jars have identical contents, but when the supertask is complete, A
's jar is empty and B
's jar contains an infinite number of balls, each of which has a number that ends with an infinite string of zeroes.