f: [0,1]--> R (reals)

f(x) = {1 if x= 1/n where nEN (element Naturals) , 0 otherwise}

Prove f is continuous at 1/pi

Thank for the help on the previous problem, I have not been able to make any progress on this problem and need help please.

Printable View

- May 11th 2013, 04:21 PMleonhartReal Analysis Prove continuous
f: [0,1]--> R (reals)

f(x) = {1 if x= 1/n where nEN (element Naturals) , 0 otherwise}

Prove f is continuous at 1/pi

Thank for the help on the previous problem, I have not been able to make any progress on this problem and need help please. - May 11th 2013, 04:29 PMGusbobRe: Real Analysis Prove continuous
Show that there is some delta neighbourhood around 1/pi which does not contain a number of the form 1/n, with n a natural number. Then the function evaluated at each point of this neighbourhood is identically zero, which is the value of f(1/pi). A quick epsilon-delta proof finishes this problem off.