I need help showing that Dirichlet's function is discontinuous on the interval (0,1).

f(x)=

{1/q if x=p/q in lowest terms with p,q in N

0 if x is irrational}

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- November 14th 2009, 09:49 PMdannyboycurtisshowing dirichlet's function is discontinuous on (0,1)
I need help showing that Dirichlet's function is discontinuous on the interval (0,1).

f(x)=

{1/q if x=p/q in lowest terms with p,q in N

0 if x is irrational} - November 15th 2009, 12:53 AMredsoxfan325
This function is continuous at irrational . To prove it's discontinuous at , let . Since for all , contains an irrational point, such that .

There's a good picture of this function on MathWorld. - November 15th 2009, 01:11 AMtonio