Comment by seanhunter

Here you go https://claude.ai/share/c8407777-1ccf-402b-9010-7bc57228b943

I asked Opus 4.8 to critique my algebra notes (these are definitely not masters level- just undergrad second year). It hallucinated an error it claimed I made in the notes and then put in a correction I didn't need because what I had written was correct.

What I said in my notes was:

   Notice that a cyclic group is a degenerate (in the sense of "smallest
   non-trivial") case of a finitely generated group where the generating set is
   a singleton.

It left-off the "non-trivial" and said that what I said was this was the smallest case of a finitely-generated group which is incorrect because it excludes the trivial group.

The point is I see the LLMs as a "smart friend"/colleague I can work with but I do think critically about what I get told and don't just take it as face value because it's not always correct for sure even in relatively basic cases like this.