The difference between Axiom and Well-formed formula

When used as nouns, axiom means a seemingly self-evident or necessary truth which is based on assumption, whereas well-formed formula means a statement that is expressed in a valid, syntactically correct, manner.

check bellow for the other definitions of Axiom and Well-formed formula

  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. Well-formed formula as a noun (logic):

    A statement that is expressed in a valid, syntactically correct, manner.

    Examples:

    "This program works correctly on all well-formed formulas but it blows up on illegal input."

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