I have these two definitions for an adherent value of a sequence
the first is : $a$ is a an adherent value for $(x_n)$ iff $$\displaystyle \forall \varepsilon>0,\forall n\in \mathbb{N},\exists n_0\geq n, d(x_{n_0},a)\leq \varepsilon$$ the second is $a$ is an adherent value for $(x_n)$ if there exists a sub sequence witch converge to $a$
But i don't know how to prove the equivalence between the two definitions