The transitive closure of a set $X$ is the smallest transitive set $\operatorname{tc}(X)$ such that $X\subseteq \operatorname{tc}(X)$

The transitive closure of a set can be constructed as follows:

Define a function $f$ on $\omega$ by $f(0)=X$ and $f(n+1)=\bigcup f(n)$ $$\operatorname{tc}(X)=\bigcup_{n<\omega} f(n)$$