Real Analysis, Lecture 4: The Least Upper Bound Property

Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Get notes and study tools at http://gosuapm.com/

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[findclue]

Typo: field -> a field.

[findclue]

@tubedudelive I don't think he needed to define an injection mapping the cuts to the real numbers since after we understood the injection between the rationals and the cuts that he defined, we can treat cuts as numbers instead of the numbers that we were using, and he and the book showed that the set of every cut is field with addition and multiplication, so now we have this perfect algebraic structure which we tempted to call R. I think he is good at explaining things in easier language.

[chessnut1987]

thank yyou

[tubedudelive]

Well, I now see that at 16:42 he corrected himself by adding an '*' to the '2' and therefore making it a cut.

[tubedudelive]

He is at times sloppy and consequently confusing. Based on his definition of cut, at 15:38 the equality should be "gamma squared = 2*", i.e. the right hand side should be a cut. The root of the problem is that he defined a cut as the subset, but he never fully developed the injection that maps the cuts to the corresponding real numbers.

[sdoken]

if anyone else is confused the way i was for a second, a lot of times he means "less than or equal to" when he says "less than". these lectures are GREAT! Praying that he will put videos of the next analysis course after this since thenlectures here cover only half of undergrad analysis.

[bimoltheorem]

good work!

[Mr123456Funnyman]

great explanation! thanks