Question: a) Let E be a subset of R. A point a R is called a cluster point of E if E (a -

a) Let E be a subset of R. A point a ∊ R is called a cluster point of E if E ∩ (a - r, a + r) contains infinitely many points for every r > 0. Prove that a is a cluster point of E if and only if for each r > 0, E ∩ (a - r, a + r)\{a) is nonempty,
b) Prove that every bounded infinite subset of R has at least one cluster point.

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