Let formula_1 be a finite set of numerical digits with cardinality formula_2 (If formula_3, then the positional number system is trivial and only represents the trivial ring), with each digit denoted as formula_4 for formula_5 is known as the radix or number base. formula_1 can be used for a signed-digit representation if it's associated with a unique function formula_7 such that formula_8 for all formula_9 is what rigorously and formally establishes how integer values are assigned to the symbols/glyphs in formula_10 One benefit of this formalism is that the definition of "the integers" (however they may be defined) is not conflated with any particular system for writing/representing them; in this way, these two distinct (albeit closely related) concepts are kept separate.