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What are theorems (lemmas, axioms, etc) exactly?
I know what a theorem is, and I know how theorems are motivated; I also know what lemmas and axioms are.
My question concerns something a little deeper.
Are these theorems and mathematical tools we have merely a consequence of the way we've defined things?
Are they discovered or created?
Feel free to share some thoughts.
I know what a theorem is, and I know how theorems are motivated; I also know what lemmas and axioms are.
My question concerns something a little deeper.
Are these theorems and mathematical tools we have merely a consequence of the way we've defined things?
Are they discovered or created?
Feel free to share some thoughts.
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