(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the Dirichelet's function defined on (0,1) by

f(x)= 0 is x is irrational

and

f(x)= 1/q if x=p/q

where p and q are positive integers with no common factors. Show that lim f(x) for any x in (0,1) is 0

3. The attempt at a solution

Here is the first line of the proof the professor gave us.

"Let eps>0 and n so large that (1/n)<=eps, where n is a natural number. The only numbers x for which f(x) can > eps are 1/2, 1/3, 2/3, ..., 1/n, ...(n-1)/n. "

I don't understand how the any p/q with n as q can be greater than epsilon is n is chosen so large that 1/n <=eps.

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# Homework Help: Does this make sense?

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