The full set of axioms for integer arithmetic may be found in the Bible, as demonstrated by J.C. Keister in [http://www.trinityfoundation.org/PDF/027a-MathandtheBible.pdf this article]. For example, [[Luke 9-16 (Translated)|Luke 12:52]] is a striking statement of the commutative law for addition: "For from this point forward there will be five in one house divided, three against two, and two against three." This understanding presaged both later attempts at the axiomatization of arithmetic by Peano and the development of [[abstract algebra]] in the 19th and 20th centuries. | The full set of axioms for integer arithmetic may be found in the Bible, as demonstrated by J.C. Keister in [http://www.trinityfoundation.org/PDF/027a-MathandtheBible.pdf this article]. For example, [[Luke 9-16 (Translated)|Luke 12:52]] is a striking statement of the commutative law for addition: "For from this point forward there will be five in one house divided, three against two, and two against three." This understanding presaged both later attempts at the axiomatization of arithmetic by Peano and the development of [[abstract algebra]] in the 19th and 20th centuries. |