abstract algebra addition algebraic number american mathematical society bicomplex number biquaternion canonical form cardinal number cauchy sequence complex number construction of the real numbers dedekind cut dual number edmund landau electrical engineering equivalence class equivalence relation euclid exponentiation fundamental theorem of arithmetic giuseppe peano hypercomplex number hyperreal number imaginary number imaginary unit integer irrational number irreducible fraction isomorphism large numbers mathematics multiplication musean hypernumber natural number negative and non-negative numbers number numeral numeral system octonion order of operations ordinal number p-adic number partition of a set peano axioms polynomial quaternion rational number real number richard dedekind sedenion set-theoretic definition of natural numbers solomon feferman split-complex number split-quaternion supernatural numbers superreal number surreal number tessarine tetration total order transcendental number transfinite number vector space