Suppose f: [a, b] → R is continuous and la f = 0 for all rational x in [a, b]. Show that f(t) = 0 for all € [a,b]. (Hint

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Suppose f: [a, b] → R is continuous and la f = 0 for all rational x in [a, b]. Show that f(t) = 0 for all € [a,b]. (Hint

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Suppose F A B R Is Continuous And La F 0 For All Rational X In A B Show That F T 0 For All A B Hint 1
Suppose F A B R Is Continuous And La F 0 For All Rational X In A B Show That F T 0 For All A B Hint 1 (8.04 KiB) Viewed 23 times
Suppose f: [a, b] → R is continuous and la f = 0 for all rational x in [a, b]. Show that f(t) = 0 for all € [a,b]. (Hint: You can assume that a continuous function vanishing on a dense set is constantly zero.)
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