User blog comment:MachineGunSuper/Supertasks/@comment-30869823-20180826165634

Supertasks are just a way to reason about what happens "after" an infinite process, as MilkyWay90 explained you can't usually do them (unless if there is a proces for which the time it takes do each step does actually converge...)

As for the pi and color onces, they just aren't meaning full questions, you are asking what is the last digit of pi but pi doesn't have a last digit.

An example is this: suppose you have a counter that starts at 0 and counts in an interval of 1 and then halfs the interval each time. Which number does it display after 2? It can't be N because it would go to the next number at time 2-2^N so it can't be any number.

These questions are just meaningless.

My favorite supertask-pair goes as follows, start with an inifinite countainer of balls numbered 1,2,3,...

take an other inifinite container and at each step add the next 10 balls and remove the ball with the lowest number.

after 1 step it contains: 2,3,4,5,6,7,8,9,10 after 2 steps it contains: 3,4,5,6,...,20 after N steps it contains: N+1,N+2,...,10N

In each step you add 9 balls. What does it countain after the supertask? Nothing! Because at step N you removed ball N. So it can't contain ball N for any N!

Do the samething except this time only add 9 balls and throw the 10th one away, instead of removing a ball write an extra zero on the smallest numbered ball.

after 1 step it contains: 2,3,4,5,6,7,8,9,10 after 2 steps it contains: 3,4,5,6,...,20 after N steps it contains: N+1,N+2,...,10N

How many balls are there left now? infinitely many! Because you never remove a ball, even though at each step both process have exactly the same content!