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Let f:R->R be an increasing fucntion. Proce that lim x->c+f(x) and lim x-c-f(x) (right and left hand limits) must each exist at every point c in R.

There's more to the question, but if I can get this part solved, i'm sure the rest won't be trouble.

My original idea was to prove this by contradiction, assuming the limits don't exist, and showing this violates the increasing aspect. However, i've come to deadends each time. Proving it directly seems very difficult as well.