Fun with infinitely large numbers (Wondrous Mathematics)
|Description||Is infinity plus one bigger than infinity? Or is it still just infinity? If you were bothered by this question at some point in your life, this talk is for you. It gives you the graphical tools to decide this question for yourself without any remaining doubt. Absolutely no mathematical prerequisites needed.|
|Language|| en - English |
en - English
|Starts at||2016/12/27 15:00|
|Ends at||2016/12/27 15:45|
This talk gives a leisurely introduction to ordinal numbers and cardinal numbers, two systems for rigorously talking about infinitely large numbers. In philosophy, infinity is a somewhat fuzzy, nebulous concept ("love is infinite"). In contrast, in mathematics, we can talk rigorously about infinities. It turns out that there is an infinite tower of higher and higher infinities.
In order to enjoy the talk, absolutely no mathematical prerequisites are needed: The talk is even accessible to school children of age ten and higher (if they understand English). And still it is mathematically rigorous – we'll learn how to think about and calculate with infinities in a precise fashion. After the talk you'll be able to effortlessly converse on infinitely large numbers with your mates.
If you already know ordinal arithmetic, for instance from a course on set theory in university, then stay away from this talk, unless you want to contribute to the talk by witty remarks. You will be bored to hell.
Some talk-related resources:
- Slides from a previous installment of this talk
- Video of the talk (many thanks to @timjb)
- Notes by John Baez on ordinals
- Notes on an alternate mathematical universe which contains infinitesimal numbers (in German)
- Notes on Gödel's incompleteness theorem (an approach using ideas from computer science)
- Notes on Gödel's incompleteness theorem in German