Talk:Choice sequence

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I'll flesh this article out soon, I swears it. ILikeThings (talk) 07:58, 22 June 2008 (UTC)[reply]

"Let \alpha\in n denote the relation "the sequence α begins with the initial sequence n"" Is this notation really correct? \in is used in two different ways in the same formula. Twanvl (talk) 23:03, 13 May 2009 (UTC)[reply]

It's totally silly notation, I know. This is what I've seen in the literature, though. And I think it's used consistently throughout the article (as far as I can tell, the axiom of open data is the only place where the \in predicate is used twice, and it means the same thing in both cases). ILikeThings (talk) 22:49, 28 May 2009 (UTC)[reply]

"The axiom of density, given by:

\forall n\,\exists \alpha [\alpha \in n]

states that, for any finite prefix (encoded by) $n$ , there is some sequence $\alpha$ beginning with that prefix."

Is this correct? I think the axiom of density states the existence of a lawless sequence. Can someone check the literature?