# iTunes U albums

### Album: Foundations of Pure Mathematics

## Track: Rational numbers and irrational numbers: further results- Foundations of Pure Mathematics - Dr Joel Feinstein

**Description:**
The fifth lecture in Dr Joel Feinstein's G11FPM Foundations of Pure Mathematics module covers:
• The algebra of rational numbers: sums and products of rational numbers are rational (etc.)
• Comparison with irrational numbers: investigation of combinations of rational numbers and irrational numbers.
• Density of the rationals and the irrationals in the real line.
Note the factor 2 error in the last sketch proof, as noted in the call-out.
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-lecture5.mp4

**Duration:**
47:04

**Size:**
115945472

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