Let $$(a_n)_{n=m}^{\infty}$$ be a sequence of real numbers, let x be a real number, and let $$\epsilon > 0$$ be a real number. We say that $$x$$ is ε-adherent to $$(a_n)_{n=m}^{\infty}$$ iff there exists an $$n \ge m$$ such that [...]. We say that $$x$$ is continually ε-adherent to $$(a_n)_{n=m}^{\infty}$$ if it is ε-adherent to [...] for every $$N \ge m$$. We say that $$x$$ is a limit point or adherent point of $$(a_n)_{n=m}^{\infty}$$ if it is continually ε-adherent to [...] for every [...]