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Real Numbers: Lecture 1 (UpperBounds)

This may be considered as the first lecture on real Analysis. We assume the algebraic structure and order relations on R. We then define upper bounds and lower bounds for subsets of R and introduce subsets which are bounded above and bounded below in R. This will be followed by a lecture on LUB and GLB. 00:00 - Motivation and mandatory disclaimer. 03:09 - Definition of upper bound. 05:50 - One Example of upper bound. 08:32 - Negation of upper bound. 10:30 - Lower bound. 12:17 - Negation of Lowe bound. 14:59 - First example. 17:46 - Second example. 21:55 - Exercises. 24:20 - Definition of bounded above. 25:27 - Definition of bounded below. 27:57 - Negation of bounded above and below. 31:49- Last example of this Lecture and advise.