Mathematical logic uses the term numeral to refer to an explicit representation of numbers (almost always, of natural numbers). This use is an extension of Gritchka's "mathematical" sense: "5" is the numeral (in the decimal representation called "Indian numerals" or "Arabic numerals") of the number five. However, "17" is the numeral for seventeen in this mathematical logic sense.

More formally, "numerals" for the natural numbers are any definitions for 0 ("zero") and S ("successor") which satisfy Peano's axioms. Since any 2 models of these axioms are isomorphic, all numerals are indeed representations of the natural numbers. Examples include von Neumann numerals and other definitions from set theory (see natural numbers as sets on E2; however note also that von Neumann numerals are really "numerals" for all ordinals, not just the natural numbers), and Church numerals.