If x is a cluster point for the sequence {x_n}, there is a subsequence of {x_n} whose limit is x. The subsequence can be constructed by choosing a sequence of shrinking neighborhoods V_k about x. Since x is a cluster point, each such neighborhood contains infinitely many elements of {x_n}. By choosing a new point x_k from each neighborhood V_k, we get a subsequence {x_k} of {x_n} with lim x_k = x.
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No limit.
an infinite number; no limit
I assume you mean that the line goes through a certain point. There is no limit to how many lines you can have through the same point.
Let f be a function and a be the given point you are considering. Then,f(x) - f(a)---------------(x-a)is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.
The answer depends on the type of distribution for the data. It could be the modal class.