The formal systems of mathematics are systems in this sense. The parts numbers, variables, and signs like + and =. The rules specify ways of combining three parts to form expressions, and ways of forming expressions from other expressions, and ways of forming true sentences from expressions, and ways of forming true sentences from other true sentences. The combinations of parts, generated by such a system, are the true sentences, hence theorems, of mathematics. Any combination of parts which is not formed according to the rules is either meaningless or false