# 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 :

does not exist.

Prove that there exist sequences {p_{n}} and
{q_{n}} in E with

such that and exist, but are not equal.