I've been trying to understand what truly is an inductive definition and I came across this one I just can't figure out:
$(1)$ $ 0 \in A$
$(2)$ $ n \in A \implies n \in A$
2026-04-09 11:13:45.1775733225
Is this an inductive definition?
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As it's written, (2) is a tautology. The only element $A$ needs to have to satisfy the given conditions is $0$. So we can't use induction to prove anything else.