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Real Analysis, Lecture 1: Constructing the Rational Numbers

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Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Playlist, FAQ, writing handout, notes available at: http://analysisyawp.blogspot.c...

Channel: Education
Uploaded: November 30, 1999 at 12:00 am
Author: HarveyMuddCollegeEDU

Length: 02:06
Rating: 4.9574466
Views: 126886


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Video Comments

wberb vervev (November 30, 1999 at 12:00 am)
why real analysis is a first year course in this school...?
vinay vittal (November 30, 1999 at 12:00 am)
Thank god for the lectures , thank you! 
Prasanth Francis (November 30, 1999 at 12:00 am)
interesting way of presentation... i like it...but if he use more diagrams or representations in number line it would have been better.
Salman Bashir (November 30, 1999 at 12:00 am)
This guy is awesome. Explained everything like a hero.
Matchbox201000 (November 30, 1999 at 12:00 am)
Very good lectures on the core concepts of real analysis, great videos
isaac asimov (November 30, 1999 at 12:00 am)
Is it me or Prof. Su sounds a bit like Mr.Mackey! Great course btw.
jorge alonso (November 30, 1999 at 12:00 am)
For a more thorough study on the construction of the number fields like the reals and the complex, I recommend Edmund Landeau's Foundations of Analysis. Most of the theorems are not hard to get but the ones that serve as a basis for many constructions are hard. 
Duna Alexandru Dan (November 30, 1999 at 12:00 am)
@WorldCollections Thanks for recommending it!:)@Evan Zamir Thank you too!:)
Antony Foster (November 30, 1999 at 12:00 am)
In the discussion about Relations nothing is said as to what an ordered pair is. In fact, the instructor said it isn't a set which is false. An ordered pair (x,y) is a set namely:(x,y) =: {{x}, {x, y}}. Also, the domain and range of relations was not mentioned. I do understand that these discussions belong in a course on set theory, but the instructor did bring up set theory ideas (unions, intersections, binary relations, functions, etc) and so domain and range of relations needs to be mentioned in this lecture since his about to construct the all important "set of rationales". If you ask me, I would clearly say this lecture is set theory ( the foundation of mathematics)
Bush Ninja (November 30, 1999 at 12:00 am)
If you use a calculator to split up a line, then you are using rational fractions.If you draw a square with straight edge and compass, you can't convince me it's a square. There will always be an atom unaccounted for.

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