The singleton $\{a\}$ is the set $\{a,a\}$.
For any $X$,
\[X \neq \{X\}.\]
Proof.If $X=\{X\}$, $X\in X$, contrary to ZF#PROP-SLF.
For any $a$,
\[\big\lvert\{a\}\big\rvert = 1.\]
Proof.$\{(a,0)\}$ is a bijection from $\{a\}$ to $1$.
The singleton $\{a\}$ is the set $\{a,a\}$.
For any $X$,
\[X \neq \{X\}.\]
Proof.If $X=\{X\}$, $X\in X$, contrary to ZF#PROP-SLF.
For any $a$,
\[\big\lvert\{a\}\big\rvert = 1.\]
Proof.$\{(a,0)\}$ is a bijection from $\{a\}$ to $1$.