- #1
barksdalemc
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Homework Statement
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
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.