Math 131 083116 Lecture #01 Ordered Sets and Boundedness

Note that this series was rerecorded in 2020: those (sharper) recordings can be found at Course 7: (Rudin's) Principles of Mat....  My course plan for that series can be accessed at https://docs.google.com/spreadsheets/...

[Notes for the course and others may be downloaded at http://community.scrippscollege.edu/w....]  Heading towards the real (and complex) numbers: problems with the rational numbers (algebraic incompleteness, analytic incompleteness).  Square root of two is irrational.  Sets with no least upper bounds.  Basic set notation.  Ordered sets.  Boundedness: upper bound, lower bound, supremum, infimum.  Least upper bound property.

#leastupperbound
#orderedsets
#boundedness
#supremum
#infimum
#leastupperboundproperty

• #education
• #principles_of_analysis
• #rational_numbers
• #real_numbers
• #supremum
• #infimum
• #upper_bound
• #lower_bound
• #ordered_sets