Explain how a theorem is different from an Axiom.
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A mathematical statement that we know is true and which has a proof is a theorem. ... So if a statement is always true and doesn't need proof, it is an axiom. If it needs a proof, it is a conjecture. A statement that has been proven by logical arguments based on axioms, is a theorem.
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Theorems can be proved but axioms can't be proved as they are taken for granted.
For eg., The halves of a whole is smaller than the whole itself. This is an axiom.
Hope it helps you.
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