 Axiom of infinity (source code)

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= Axiom of infinity
{wiki}

The axiom asserts the existence of a set containing the empty set and closed under the successor operation $x\mapsto x\cup\{x\}$:
$$
\exists I\;\bigl(\varnothing\in I\land\forall x\in I\;(x\cup\{x\}\in I)\bigr).
$$
In <Zermelo–Fraenkel set theory>, this supplies a set from which the set of <natural numbers> is constructed.

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