this post was submitted on 25 Aug 2026
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Yeah, I always felt like I was either pointlessly restating the obvious or it expected me to derive the damn thing from first principles.
AI slop proof, just because I was curious if duck.ai could do it
Using the natural numbers defined from 0 by the successor operation S:
1=S(0), 2=S(1), ... , 20=S^20^(0), 40=S^40^(0)
Define a < b to mean that there exists a natural number k such that
a+k=b.
Take a=20 and k=20. By repeated addition,
20+20=40.
Since 20 is a natural number, there exists a natural number k such that
20+k=40.
Therefore, by the definition of the ordering relation,
20<40.
(Is it correct? Fuck if I know!)
A.I. is proving that 20<40 by:
Honestly since it's such a simple equation, in real life you could just say 20<40 because 20<40. You don't really need to prove anything, the proof is in the logical operator. The homework question is dumb because it isn't clear what they're asking for.