f_n converges to f which is 1 at the beggining f_n is 0 but when n goes to infinity its 1 so why sup(f_n(x)-f(x))=1 ? f is allways 1 but f_n is 0 and going to one so the supremumum of their difference is 0 not 1 ?
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Originally Posted by transgalactic f_n converges to f which is 1 at the beggining f_n is 0 but when n goes to infinity its 1 so why sup(f_n(x)-f(x))=1 ? f is allways 1 but f_n is 0 and going to one so the supremumum of their difference is 0 not 1 ? you are taking the supremum of the difference. Not just . So you are looking for the least upper bound of the differences.
exacty in one case its 1-1 in the other its 0-1 the supremum is 0
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