 Infinity: There is an infinite set. Zermelo’s original formulation asserted the existence of a set containing \(\varnothing\) and closed under the singleton operation: \(\{\varnothing ,\{\varnothing \},\{\{\varnothing \}\}, \ldots \}\). It is now more usual to assert the existence of a set which contains \(\varnothing\) and is closed under the von Neumann successor operation \(x \mapsto x \cup \{x\}\). (Neither of these axioms implies the other in the presence of the other axioms, though they yield theories with the same mathematical strength).