Zählen jenseits des Unendlichen

Teaser Image Zählen jenseits des Unendlichen - Bis zu Epsilon Null (2007) 2 min
ID: 2007-4
Director: Oliver Deiser
Author: Oliver Deiser
Country: ger
Age Rating: 0
Distributor: Springer Verlag
Genres: Short Movie, Animated Movie
Languages: German, English

The most basic mathematical process is counting:
0, 1, 2, 3, 4, 5, 6, ...
In the 1870’s, the mathematician Georg Cantor invented (or found) how to count beyond infinity:
0, 1, 2, 3, ..., ω, ω+1, ...
The short film visualizes the transfinite numbers up to a number which is called ε0.

There are many more transfinite numbers beyond ε0. In any case, we can only visualize a tiny initial segment of all infinite numbers. It took half a century until John von Neumann gave the first rigorous definition of transfinite numbers inside axiomatic set theory. Still today, the concept of counting beyond infinity remains an intellectual challenge, even for professional mathematicians. It is fair to say that Cantor’s set theory marks the beginning of modern mathematics, where infinite objects coexist with finite ones. And the transfinite numbers form the spine of the universe of infinite sets in much the same way as the non-negative integers do in the realm of arithmetic and finite combinatorics. They are the mathematical key to understand infinity, and their richness and structure is a matter of research, debate, and fascination.

This film is included in the compilation MathFilm 2008 DVD.