Are there any theorems that can only be proved by induction? Induction seems to be proof by technicality.
2026-05-05 10:43:42.1777977822
Is Proof By Induction Necessary?
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What set of axioms are you using? If you use the Peano Axioms, you can't prove much without induction. In particular, the commutative and associative properties of addition and multiplication require induction. The inverted addition proof that you mention needs a lot of work to justify if you go all the way back to the axioms. If we don't go back to the axioms we rely on a lot of intuitive understanding of the naturals.