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There are four main properties of Supremum that we should be aware of. In the first video we will see how the supremum of a set a+S is equal to the sum of a and supremum(S).
In the second video we will lear how to relate supremum and infimum of two distinct related sets. We will check when and in what conditions will SupA < Inf B for any given sets A and B.
In the third video we will try and understand what is the relation between the Supremum of any two bounded functions . if f(x)<g(x) for all x, then what is the relationship between the supremum of f and g.
Finally, in the fourth property we twist the previous property and check the relationship between these two functions given the condition that f(x)<g(y) for all x and y. Continue reading
