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Question: let e be a nonempty subset of reals and let...

Question details

Let E be a nonempty subset of Reals and let p be a limit point of E. Suppose f is a bounded real-valued function on E having the property that :

lim f(x) does not exist.

Prove that there exist sequences {pn} and {qn} in E with

lim pn- lim qn- p such that lim f(pn) and lim f(gn) exist, but are not equal.

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