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Homework Statement
f is a function with the property that every point of discontinuity is removable. There are infinitely many such points in f's domain. Define [tex] g(x) = \lim_{ y \to x } f(y) [/tex]. Prove g is continuous
The Attempt at a Solution
I wanted to maybe conclude something from showing g is bounded but I didn't really get anything there. I was wondering if you could give me a hint, but DON'T GIVE ME A SOLUTION yet. Should I be using straight forward definition or take some other route?