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  3. let f : [0, 1] ? r and suppose that, for all finit

Let f : [0, 1] ? R and suppose that, for all finite subsets of [0,...

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Advance Math

Let f : [0, 1] ? R and suppose that, for all finite subsets of[0, 1], 0 ? x1 < x2 < · · · < xn ? 1,

we have |f(x1) + f(x2) + · · · + f(xn)| ? 1. Let S := {x ? [0,1] : f(x) ?= 0}. Show that S is countable

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