Show that the set of functions from the positive integers to the set {0, 1, 2, 3,4, 5, 6, 7, 8, 9} is uncountable. [Hint: First set up a one-to-one correspondence between the set of real numbers between 0 and 1 and a subset of these functions. Do this by associating to the real number 0.d1 d2 .. .dn ... the function f with f(n) = dn.]
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