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Update peano-derivative.md

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Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
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Alexa Amundson
2026-02-27 01:48:27 -06:00
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@@ -120,7 +120,8 @@ To prove PA wrong from inside PA, you would need to derive:
This has not been done in over a century of scrutiny. It would not win a prize.
It would break mathematics itself — every theorem built on PA would collapse with it.
The consistency of PA is assumed (and follows from ZFC), not merely hoped for.
The consistency of PA is assumed and can be proved in stronger systems such as ZFC,
assuming those systems are themselves consistent—not merely hoped for.
What has been done is something different:
- Extending the notation (1_1 instead of 1): not a contradiction, a redefinition