User talk:Lord Farin/Backup/Definition:Formal Language

Definition is weird
Hm, this is not how I learnt the definition of a formal language. Currently this reads:

A formal language is a structure which contains:
 * An alphabet of symbols;
 * A set of words made up of symbols from that alphabet;
 * A formal grammar which determines which words belong to the formal language and which do not.

The third bullet point seems to me extraneous. By my reckoning, a formal language consists of: As I understand it, a grammar is a way to construct a set such as $W$ and thus to define a language; what use is it to include a grammar and a set of words in the definition of a formal language? — Timwi (talk) 22:36, 18 December 2012 (UTC)
 * a set $S$ (the alphabet) and
 * a set of words $W \subseteq \left\{ { \left({ x_1, x_2, ..., x_n }\right) : \forall i, x_i \in S}\right\}$