Transcendental numbers powered by Cantor's infinities

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by Super User, 5 months ago
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In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track way to pinpoint a transcendental number and to show that it is really transcendental. Also find out why there are a lot more transcendental numbers than numbers that we usually think of as numbers, and this despite the fact that it is super tough to show the transcendence of any number of interest such as pi or e. Also featuring an animated introduction to countable and uncountable infinities, Joseph Liouville's ocean of zeros constant, and much more.

Here is a link to one of Georg Cantor's first papers on his theory of infinite sets. Interestingly it deals with the construction of transcendental numbers!
Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen", Journal für die Reine und Angewandte Mathematik, 77: 258–262
http://gdz.sub.uni-goettingen.de/pdfcache/PPN243919689_0077/PPN243919689_0077___LOG_0014.pdf

Here is the link to the free course on measure theory by my friend Marty Ross who I also like to thank for his help with finetuning this video:
http://maths.org.au/index.php/2013/105-events/education-events-2006/316-ice-emamsi-summer-school-2006
(it's the last collection of videos at the bottom of the linked page).

Thank you also very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.

Enjoy!

Burkard