What is Axom's Theorem ?
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Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics
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All axioms are theorems.
Theorems, however, include not only axioms, but also sentences derivable from those axioms by means of inference rules. That is why the formal theory of a language system is the set of its axioms closed under logical consequence.
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