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Having discussed the least upper bound of a bounded above set, in the first video today we will discuss the concept of the greatest lower bound of a bounded below set.
In the second video we will show with examples that we might have many upper bounds and lower bounds but the supremum and infimum are unique always.
Finally we will work out the formal characterization of the supremum for any set. This is another way of stating the definition of supremum, which is that no number smaller than the supremum can be an upper bound of the given set. Continue reading →