Example
190
[290]Examples of transitive sets are:
\begin{align*} \{ \} = 0 \\ \big\{ \{ \} \big\} = 1, \\ \Big\{ \{ \} ,\big\{ \{ \} \big\} \Big\} = 2,\\ \bigg\{ \{ \} ,\big\{ \{ \} \big\} ,\Big\{ \big\{ \{ \} \big\} \Big\} \bigg\} , \\ \Bigg\{ \{ \} ,\big\{ \{ \} \big\} ,\Big\{ \big\{ \{ \} \big\} \Big\} , \bigg\{ \Big\{ \big\{ \{ \} \big\} \Big\} \bigg\} \Bigg\} ,\\ ...\\ \bigg\{ \{ \} , \big\{ \{ \} \big\} , \Big\{ \{ \} , \big\{ \{ \} \big\} \Big\} \bigg\} =3\\ \bigg\{ \{ \} , \big\{ \{ \} \big\} , \Big\{ \big\{ \{ \} \big\} \Big\} ,\Big\{ \{ \} ,\big\{ \{ \} \big\} \Big\} \bigg\} ,\\ .... \end{align*}
Comparing with [291] note that there are transitive sets that are not natural numbers.