View source for Inductive set

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==Definition==
Let {{M|I}} be a [[set]]. We call {{M|I}} an ''inductive set'' if{{rITSTHJ}} both of the following properties hold:
# {{M|\emptyset\in I}} - often written {{M|0\in I}} as {{M|0}} is represented by the {{emptyset}} - and
# {{M|\forall n[n\in I\implies}}[[Successor of a set|{{M|S(n)}}]]{{M|\in I]}} - often written as "if {{M|n\in I}} then {{M|(n+1)\in I}}" 
#* {{M|S(x)}} denotes the [[successor set]] of {{M|X}}
{{Caveat|Note that this certainly describes the natural numbers as we require {{M|\emptyset\in I}}, so they're in there. The problem is that rule 2 seems to require that for every element {{M|n}} that {{M|n\cup\{n\} }} is in there too.}} - this seems to be intended{{rSTTJ}}
==References==
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