Definition talk:Word

I am having a problem here at the moment. Awodey says:


 * "Let $A$ be an alphabet, that is, a set $A = \left\{{a, b, c, \ldots}\right\}$. A word over $A$ is a finite sequence of letters."

It seems not to fit in either of the definitions currently up, while it is intimately connected to both. It pertains to the same stuff Jshflynn has been putting on his user domain. Should I just add another definition for it? If so, what to call it? Maybe introduce a new category 'Finite Sequences' so that we in passing have a place for Jshflynn's stuff to move in due time? My def would become Definition:Word (Finite Sequences) in that case. Thoughts? --Lord_Farin 14:04, 15 August 2012 (UTC)


 * Hi L_F. If you wish to do so you may quote: Introduction to Formal Language Theory by M.A.Harrison. There is still plenty of work to be done for anyone who is interested. Just see Chapter 2 of the following book which is freely available on Google Books: . I will continue contributing as soon I have finished writing up some other unrelated document. --Jshflynn 15:34, 15 August 2012 (UTC)


 * In what way is it different from the definition as in Definition:Word (Formal Systems)? In my eyes it's the same. Again, am I missing something? Except for some reason Definition:Finite String has been redirected to Definition:Word: what was that all about? --prime mover 16:35, 15 August 2012 (UTC)


 * Instead of alphabet being defined as some specified collection of symbols pertaining to a formal language, it is just a set. Thus, the formal language def is an instance of the one purported by me, Jshflynn, Harrison and Awodey (in no particular order). It would be unfitting to add it there since it does not pertain to formal languages. --Lord_Farin 16:50, 15 August 2012 (UTC)

If an alphabet is just a set, then why not just say "set"? From what I understand, an "alphabet" is a set which is nested in a formal language. In the same way, if a "word" is just a sequence of elements of a set, then why not just use the word "sequence?" Otherwise you have multiple words for the same thing, the only difference being the label on the category of mathematics that the definition is made in.--prime mover 18:09, 15 August 2012 (UTC)


 * An alphabet is a finite non-empty set from the definitions I've seen. Words are finite sequences over an alphabet. I dislike synonyms in mathematics as well. It's unfortunate there's no W3C like organisation for mathematics :) --Jshflynn 18:22, 15 August 2012 (UTC)


 * yes-but-yes-but ... the only reason for calling it an "alphabet" is to use it in the context of a formal language. --prime mover 18:30, 15 August 2012 (UTC)


 * Okay... (what the heck does "yes-but-yes-but" mean?). It's probably restricted to being a finite non-empty set because they are used in computing by finite automata. I haven't looked so far into it yet. I'll just go along with whatever wording you guys see as most fitting. After all, it's important that the most potent contributors of the site are most comfortable with the vocabulary of the site. Peace. --Jshflynn 18:50, 15 August 2012 (UTC)


 * Fair enough. I will amend existing pages as appropriate. Apologies for generated confusion. --Lord_Farin 18:12, 15 August 2012 (UTC)


 * OK - I will swing by again when I revisit the source works to define their linear flow. --prime mover 18:15, 15 August 2012 (UTC)

Definition loop
finite string and word are defined circularly. Nowhere does it tell me how to make or recognize a finite string. Dfeuer (talk) 19:22, 19 December 2012 (UTC)


 * That help? Thanks for noticing. --Lord_Farin (talk) 19:27, 19 December 2012 (UTC)


 * Better, but not good. Finite string redirects to word, which is a disambiguation page containing a link to finite string. The whole thing is a mess because the definition of word invokes the formal system containing it, which is broken. Another difficulty is that formal languages are used to formalize things like logic and set theory, and our definition of finite sequence depends on the notions of "mapping" and "natural numbers". --Dfeuer (talk) 20:31, 19 December 2012 (UTC)