accumulation points in $\mathbb R$

Question

Consider the subset $A = [a, b)$ of $\mathbb R$. Then it is easily verified that every element in $[a, b)$ is a limit point of $A$. The point $b$ is also a limit point of $A$. Why?

Answer 1

Because every open interval centered at $b$ contained infinitely many points of $[a,b).$

In other words b is the limit of the sequence $$\{b-1/n\}_{n=k}^{\infty}$$ for some $k>0.$