TITLE: Is a set containing only ONE element equal to the element itself?
QUESTION [5 upvotes]: I know this may sound like a silly question, but suppose $\space S \space$ is a set such that:
$$S= \{ 2 \}$$
Does this mean $\space S \space$ is just equal to the number $\space 2$?
OR
Is $\space 2 \space$ just an element in the set $\space S \space$ and not actually equal to the set itself?

REPLY [4 votes]: $S$ is not equal to $2$. As another example, $\{\emptyset\}$ has exactly one element (teh empty set) and therefore differs form its only element $\emptyset$ (which has no elements at all).