The difference between Axiom and Axiom of choice

When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas axiom of choice means one of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.

check bellow for the other definitions of Axiom and Axiom of choice

  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. Axiom of choice as a noun (set theory):

    One of the axioms of set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty; any version of said axiom, for example specifying the cardinality of the number of sets from which choices are made.

    Examples:

    "The axiom of choice is logically equivalent to the assertion that every vector space has a basis."

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