I want to clarify the definition of limit point and accumulation point.
According to many of my text books they are synonymous that is $x$ is a limit/accumulation point of set $A$ if open ball $B(x, r)$ contains an an element of $A$ distinct from $x$.
But from one of the problems in Aksoy: A Problem Book in Real Analysis says:
Show that if $x \in (M,d)$ is an accumulation point of $A$, then $x$ is a limit point
of $A$. Is the converse true?
So what is the definition?
