Stochastic Supertasks

Supertasks allow you to accomplish an infinite number of tasks in a finite amount of time. Find out how these paradoxical feats get even stranger once randomness is introduced. What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in.

Crisis in the Foundation of Mathematics

What if the foundation that all of mathematics is built upon isn’t as firm as we thought it was?

Note: The natural numbers sometimes include zero and sometimes don’t — it depends on how you define it. Within logic, zero is always included as a natural number.

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