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Aside, it's a shape that hypothesis in math (axiom) is the opposite of hypothesis in science (claim to test)



Not really. The words are used in closely analogous ways. But the "hypothesis" in "continuum hypothesis" is part of the name of the continuum hypothesis, carried over from a time when we didn't know the answer.

Names are just names. Euclid's Algorithm is an algorithm. The Division Algorithm is a theorem.




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