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0 pointsMrDrDr4d ago0 comments

> “incompleteness theorems” established that no formal system of mathematics — no finite set of rules, or axioms, from which everything is supposed to follow — can ever be complete.'

There is usually a 'not sufficiently complex' clause in that definition. Presburger arithmetic is complete: https://en.wikipedia.org/wiki/Presburger_arithmetic

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__MatrixMan__4d ago

Right, you need to be able to construct numbers for Gödel's proof to apply.

Hilbert's incidence geometry, for instance, is consistent and complete. It's just rather small.

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__MatrixMan__4d ago

Right, you need to be able to construct numbers for Gödel's proof to apply.

Hilbert's incidence geometry, for instance, is consistent and complete. It's just rather small.

j / k navigate · click thread line to collapse