verb
1. To ask, demand, or claim.
2. To claim or assume the existence or truth of, esp. as a basis for reasoning or arguing.
3. To assume without proof, or as self-evident; take for granted.
4. Mathematics, Logic. to assume as a postulate.

noun
5. Something taken as self-evident or assumed without proof as a basis for reasoning.
6. Mathematics, Logic. a proposition that requires no proof, being self-evident, or that is for a specific purpose assumed true, and that is used in the proof of other propositions; axiom.
7. A fundamental principle.
8. A necessary condition; prerequisite.
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