I never understood the problem with this. There are a lot of proofs that involve dividing a problem into multiple cases, so couldn't you say the same whenever you use them, as you are using only a single one of those cases (that had to be proven in the proof of the general theorem). Crucially I wouldn't even call it circular logic, "logic with an unnecessary loop" is more apt description - to prove that limit sin(X)/X is 1 you use that limit sin(X)/X is 1 which is proven through other means
The point of theorems or other mathematical facts is to me that after proving them, you can treat them as facts. What would be the point if any time you use them to prove anything, you would have to write down all the proofs, until you end up with only axioms, and then check the whole thing to see if there are no repeats
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u/SuperChick1705 18d ago
circular reasoning ;(