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Axiom of Infinity**

One of the Zermelo-Fraenkel axioms of set theory, which asserts the existence of an infinite set, which has the same cardinality as the natural numbers. \(\exists I:(\emptyset\in I\land\forall x:x\in I\Rightarrow x\cup\{x\}\in I\). As such, \(I\) contains \(\emptyset,\:\{\emptyset\},\:\{\emptyset,\{\emptyset\}\},\:\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\},...\) and so on.