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Definitions written in symbols:
Given a sequence xn, we say that x is a cluster point for xn if [itex](\forall \epsilon >0)(\forall N)(\exists n>N)(\vert x-x_{n} \vert <\epsilon)[/itex].
Given a sequence xn, we say that xn converges to x if [itex](\forall \epsilon >0)(\exists N)(\forall n>N)(\vert x-x_{n} \vert <\epsilon)[/itex].
Given a sequence xn, we say that x is a cluster point for xn if [itex](\forall \epsilon >0)(\forall N)(\exists n>N)(\vert x-x_{n} \vert <\epsilon)[/itex].
Given a sequence xn, we say that xn converges to x if [itex](\forall \epsilon >0)(\exists N)(\forall n>N)(\vert x-x_{n} \vert <\epsilon)[/itex].