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