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Got it. thanks a lot, that was perfect.

Homework Statement Let f: R -> R be a continuous function such that f '(x) exists for all x =/= 0 . Say also that the limit of f '(x) as x goes to 0 exists and is equal to L. Must f '(0) exist as well? Prove or disprove. The Attempt at a Solution I can't come up with a proof or...

Hi PFers, What I'm referring to is on p. 32 of Pugh's Real Mathematical Analysis. (trying to begin study early for this class as I've heard it's a toughie) Basically, Pugh proves the uncountability of a closed interval [a,b] of real numbers using a geometric construction which pairs each...