Computing ruler function, Prove that f(x) is continuous at

Computing ruler function

Reference no: EM13122502

1. Every rational x can be written in the form x = m/n, where n > 0, and m and n are integers without any common divisors. When x = 0, we take n = 1. Consider the function f defined on the reals where f(x) = 0 when x is irrational and f(x)= 1/n when x =m/n

a. Prove that f(x) is continuous at every irrational point and discontinuous at every rational point

b. Show that f is integrable on [0,1]

Reference no: EM13122502

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