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Album: Foundations of Pure Mathematics

Track: Countability and uncountability - Foundations of Pure Mathematics - Dr Joel Feinstein


Description: The twentieth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers countability in terms of injections and surjections. The Cartesian product of two countable sets is countable. The set of rational numbers is countable. A countable union of countable sets is countable. Intervals of real numbers: the interval (0, 1) is uncountable (proved using Cantor’s diagonal argument), and it follows that every non-degenerate interval is uncountable. These videos are also available on YouTube at: https://www.youtube.com/playlist?list=PLpRE0Zu_k-BzsKBqQ-HEqD6WVLIHSNuXa Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.

Keywords: pure mathematics, relations, functions, countable and uncountable sets, set theory, binomial coefficients

Author: The University of Nottingham

Category: Mathematics

Web page: http://www.nottingham.ac.uk/mathematics

Thumbnail: http://itunesu.nottingham.ac.uk/media/Mathematics/FoundationsofPureMathematics/images/mathematics-FPM14.jpg

Track media file: http://itunesu.nottingham.ac.uk/media/Mathematics/FoundationsofPureMathematics/video/g11fpm-lecture20.mp4

Duration: 47:45

Size: 405815296

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