Infinity

Infinitely large quantities can arise in mathematics, physics, game theory and philosophy. Those need to be handled with care if one wants to avoid paradoxes. This is a beginner's introduction to taming inf.

This will be a guided tour to a variety of occurrences of infinite quantities when counting, sorting, playing games, philosophising about arrows and turtles and when computing scattering of elementary particles. In each situation, I will explain some tools to control these infinities and how to get sensible answers to sensible questions. We will see really big sets, understand how to add 1 to infinity and how to take infinity to the infinite power, play games that are worth infinite amounts, how to add 1+2+3+ and so on to obtain -1/12 and why it is often easier to pretend something is infinite when it actually is not. Along the way, we will learn from Aristotle, Cantor, Hilbert, Feynman, Conway and what they contributed to this infinitely interesting subject. They audience should be willing to bend their mind but will not need anything but a bit of high-school mathematics.