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When this news came out I amused myself by asking Claude to prove that 0.999... != 1. First it did so for the hyperreals. To do it for the reals I had to tell it it was allowed to make mistakes, although it didn't end up interestingly wrong - just very fuzzy and vague.

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Actually it's not true for the hyperreals either, though this is a common misconception. It's extremely easy for me to believe that an llm would produce a "proof" and that people would fall for it.

I don't know if I fell for it - my response was "LOL, I sure can't tell you if this one is right or wrong". I guess that makes it more convincing than the proof for the reals.

Fable, prove that for every positive integer n, repeatedly dividing by 2 if even or multiplying by 3 and adding 1 if odd will always eventually reduce the sequence to 1.

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