The difference between Axiom and Axiom of regularity
When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas axiom of regularity means one of the axioms in axiomatic set theory, equivalent to the statement that every non-empty set contains a member that is disjoint from that set.
check bellow for the other definitions of Axiom and Axiom of regularity
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Axiom as a noun (philosophy):
A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
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Axiom as a noun (logic, mathematics, proof theory):
A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
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Axiom as a noun:
An established principle in some artistic practice or science that is universally received.
Examples:
"The axioms of political economy cannot be considered absolute truths."
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Axiom of regularity as a noun (set theory):
One of the axioms in axiomatic set theory, equivalent to the statement that every non-empty set contains a member that is disjoint from that set.