This is a recording of a popular maths talk.

These taster sessions should be particularly useful for students who are thinking of applying to study maths at university.

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What does infinity mean to you? Did you know that infinity comes in different sizes? This talk explains this idea in a visual way, using the concept of an infinite hotel, which was first discussed by David Hilbert. Hilbert was inspired by the fundamental work of Georg Cantor on set theory.

In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the final section, using Cantor's diagonal argument.

Speaker: Dr Joel Feinstein (https://www.nottingham.ac.uk/mathematics/people/joel.feinstein)

This version of the talk was originally presented as part of Virtually Nottingham in 2020 (https://tinyurl.com/uonmathsvod).

Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. Currently he is the Teaching Support Officer and the Outreach Officer in the School of Mathematical Sciences, and he teaches the first-year module Foundations of Pure Mathematics. His main research area is Functional Analysis, and especially Commutative Banach Algebras. In particular he studies curious mathematical shapes such as Swiss cheeses. You can find his blog at https://explainingmaths.wordpress.com/

Thanks to Helen Preston for converting Dr Feinstein's pdf presentation to a PowerPoint presentation.