metanumeral

A metanumeral is a term used in certain theoretical computer science contexts, particularly in formal language theory and computability theory. It refers to a way of encoding numbers or other mathematical objects using the structure of a formal language, rather than a direct numerical representation. Essentially, a metanumeral is a string of symbols from a specific alphabet that, when interpreted according to a predefined set of rules, corresponds to a particular number or value.

The concept of a metanumeral is closely related to Gödel numbering, where natural numbers are assigned to symbols, formulas, and sequences of formulas in a formal system. However, metanumerals are often more general, allowing for the encoding of a wider range of entities or using different encoding schemes. The "meta" prefix suggests that it is a numbering or representation *about* numbers or other mathematical objects, existing at a higher level of abstraction.

In practice, metanumerals can be used to represent the steps of a computation, the states of a Turing machine, or the structure of a program. By converting these computational entities into strings, they can then be manipulated and analyzed using the tools of formal language theory, such as automata and grammars. This allows for the formal study of the properties of computation and the decidability of various problems. The specific alphabet and rules used to form a metanumeral depend entirely on the context and the particular encoding scheme being employed.