The difference between Axiom and Completeness axiom

When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas completeness axiom means the following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).

check bellow for the other definitions of Axiom and Completeness axiom

  1. 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.

  2. 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).

  3. 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."

  1. Completeness axiom as a noun (mathematics):

    The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).

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