Math Club - The Bizarre World of Infinities

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Meeting ID: 936 7558 2095

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Thursday, November 5, 2020 - 18:00


Speaker Information
Thomas Gilton
University of Pittsburgh

Abstract or Additional Information

Infinities come in a bewildering and bizarre variety; in this talk I will introduce you to the world of infinities. In the first part, we will discuss a few headache-inducing thought experiments, ones involving such peculiar characters as infinite hotels ("No Vacancy; Everyone Welcome!"), infinitely-many grim reapers (watch out!), and prisoners trying to escape by making enough correct guesses (they will escape!). In the second part, we will take a more careful, mathematical look at infinities, showing in particular that there are plenty of different infinities. If time permits we will discuss the fact that many of the natural questions you'd like to ask about these infinities (such as whether there are infinities "in between" countable infinity and the size of the real numbers), cannot be decided in the standard axiom system of mathematics. Come ready to think and participate!