mathematics

Supertask

Imagine, that you have a computer which speeds up by factor of 2 after every CPU tick.

This is a hardware needed to execute a so called supertask. Infinitely many operations in a finite amount of time.

Consult Google and Wikipedia about supertasks and come back, if you are not familiar with this topic.

Now, welcome back for those who needed Wikipedia’s advice. We are going to sort all the decimals of number Pi after the decimal point with a supertask, to get 3.

Pi is the input and 3 is the output of the super-sort-function.

Then we will sort the list of all natural numbers in the reverse order to get what? Which number will be the first in the now sorted list, when the super-sort-function has completed in 2 nanoseconds? There is no biggest natural number to be placed where number 1 used to be. And no the second biggest natural number to be placed where the number 2 used to be. And so on.

This is in a nutshell , my problem with infinity. That’s why I am a finitist. Cantor was a fool.

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