7.3 The supremum and the infimum of a set

Related videos:

0:00 Introduction
0:13 Why is maximum insufficient?
1:21 Upper bound
2:06 Supremum definition
3:02 Supremum vs. Maximum
3:29 Bounded above
3:50 Infimum and other equivalents
4:40 Least upper bound principle

[raghualluri]

Just curious, would one proceed on to prove this theorem by making use of the method in which the real numbers are constructed. In other words, would one proceed to prove this theorem with the idea of Dedekind Cuts?

[ziqiwenm]

Sir, I have a question. In 3:21, definition4. is "A is bounded above means that it has at least one upper bound". Then, in 4:59, the L.U.B principle says that (A is bounded above and A is not empty) can imply A has a least upper bound. I wonder if A is an empty set, whether A has an upper bound; if it does, then why this upper bound is not the least upper bound?

[poorvisharma]

While defining lower bound, it'll become x > c right? Not >=