The difference between Axiom and Axiom of pairing
When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas axiom of pairing means one of the axioms in axiomatic set theory, equivalent to the statement that if two sets exist, there exists a set with those two sets as its elements.
check bellow for the other definitions of Axiom and Axiom of pairing
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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 pairing as a noun (set theory):
One of the axioms in axiomatic set theory, equivalent to the statement that if two sets exist, there exists a set with those two sets as its elements.