TITLE: The phrases "has ... in " vs. "contains ... of" in Baby Rudin
QUESTION [5 upvotes]: Consider the following two statements. (Assume $E \subseteq K$.)

$E$ has a limit point in $K$.

vs.

$E$ contains a limit point of $K$.

What do they each mean and how are they different?

REPLY [7 votes]: The first one means that there is a limit point of $E$, say $x$, where $x\in K$.
The second one means that there is a limit point of $K$, say $y$, where $y\in E$.