Is $\{ \emptyset \}$ is a subset of set $\{ \emptyset, 1, 2, 3 \}$?

Question

Is $\{ \emptyset \}$ a subset of set $\{ \emptyset, 1, 2, 3 \}$? I know that empty set is subset of every set, but what about $\{ \emptyset \}$? What if 'right set' was just $\{1, 2, 3\}$? Will it still be true that $\{ \emptyset \}$ is a subset of set $\{1, 2, 3\}$?

Answer 1

If you are asking about $\emptyset$, then it is indeed the subset of any set.

If you are asking about $E = \{\emptyset, 1,2,3\}$, then $\emptyset \in E$ and $\emptyset \subset E$.

Moreover, if $S = \{\emptyset\}$ then $S \subset E$.

Answer 2

The set $\{x\}$ is a subset of $\{a,b,c\}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, $\{\emptyset\}\nsubseteq\{1,2,3\}$. But $\{\emptyset\}\subseteq\{\emptyset, 1,2,3\}$

Remark: The most usual construction of $\Bbb N$ from ZFC defines $0=\emptyset$ and $1=\{\emptyset\}$.