Difference between revisions of "Inductive set"
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[hide]Definition
Let I be a set. We call I an inductive set if[1] both of the following properties hold:
- ∅∈I - often written 0∈I as 0 is represented by the ∅ - and
- ∀n[n∈I⟹S(n)∈I] - often written as "if n∈I then (n+1)∈I"
- S(x) denotes the successor set of X
Caveat:Note that this certainly describes the natural numbers as we require ∅∈I, so they're in there. The problem is that rule 2 seems to require that for every element n that n∪{n} is in there too. - this seems to be intended[2]
