[[Material set theory]]
# Axiom of Infinity

The **Axiom of Infinity** is a possible axiom of [[Material set theory]] asserting the existence of an infinite set: #m/def/set/zf 
$$
\begin{align*}
(\exists \shood \omega)[\0 \in \omega \land (\forall x \in \omega)[\{ x \} \in \omega]]
\end{align*}
$$
which is to say, there exists a set $\omega$ containing the [[empty set]] and the singleton of each of its elements.

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#state/tidy | #lang/en | #SemBr