A) Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show that f is discontin
Question: A) Let f(x) = 1 for rational numbers x and f(x) = 0 for irrational numbers. Show that f is discontinuous at every x in 
.
Hint: Let x 
. Select a sequence (xn) such that lim xn = x,
xn is rational for even n, and xn is irrational for odd n. Then f (xn) is 1 for even n and 0 for odd n,
so (f (xn)) cannot converge.
B) Let h(x) = x for rational numbers x and h(x) = 0 for irrational numbers. Show that h is continuous at x = 0 and at no other point.
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Solution Format: Word Document
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