Sup notes
WebOct 25, 2014 · 3. For a given interval I, a supremum is the least upper bound on I. (Infimum is the greatest lower bound). So, if you have a function f over I, you would find the max of f over I to get a supremum, or find the min of f to get an infimum. Here's a worked out example: f ( x) = x over the interval ( 3, 5) is shown in gray. WebProving rigorously the supremum of a set. Suppose ∅ ≠ A ⊂ R. Let A = [ 0, 2). Prove that sup A = 2. A is the half open interval [ 0, 2) and so all the x i ∈ A look like 0 ≤ x i < 2 so clearly 2 is an upper bound. To show it is the l e a s t upper bound, suppose that 2 ≠ sup A, that is there exists a number M < 2 for some real M ...
Sup notes
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