Question: what is the difference between cluster point and limit point?
Answer: So whenever S⊆X, where (X,d) is the metric space, then p∈X is called a limit point of S when for all r>0, S∩Mr(p)≠∅; p is called a cluster point of S when for all r>0 the set S∩Mr(p) is infinite, and S condenses at p (people also say that p is a condensation point of S, which is more analogous to the previous names) ...